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c,\TY Q^
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KNOW YOUR OWN SHIP:
A SIMPLE EXPLANATION
OP
THE STABILITY, TRIM, CONSTRUCTION, TONNAGE, AND
FREEBOARD OF SHIPS, TOGETHER WITH A FULLY
WORKED OUT SET OF THE USUAL SHIP
CALCULA TIONS (FROM DRA WINGS).
SPECIALLY ARRANGED FOR THE USE OF SHIPS' OFFICERS,
SUPERINTENDENTS, ENGINEERS, DRAUGHTSMEN,
AND OTHERS.
BY
THOMAS WALTON,
LATE LECTURER ON NAVAL ARCHITECTURE TO SHIPS' OFFICERS AND STUDENTS
IN THE GOVERNMENT NAVIGATION SCHOOL, LEITH, AND IN
MIDDLESBROUGH SCIENCE SCHOOL;
AUTHOR OF
"CONSTRUCTION AND MAINTENANCE OP SHIPS BUILT OP STEEL.
Witb IFlumetoud ^Uudttatfona.
FOURTH EDITION. GREATLY ENLARGED.
LONDON:
CHARLES GRIFFIN AND COMPANY, LIMITED;
EXETER STREET, STRAND.
1899.
[All nights Reserved,]
/9\i
■vrA
, W2. 4-
PREFACE TO FOURTH EDITION.
During the three years which have elapsed since the First
Edition of this work was issued, the Author has received
numerous responses to the invitation then given for "sug-
gestions and communications." These have come from ships'
ofl&cers, engineers, and from students of naval architecture,
working in shipyards. Though the original intention was to
exclude the somewhat elaborate calculations involved in arriv-
ing at many of the conclusions dealt with in this work — dis-
placement, moment of inertia, righting moment of stability,
etc., etc., — the communications received have proved beyond
doubt that such calculations would be welcomed by a very
large section of readers as a valuable addition to the book
The author has been agreeably surprised to discover that
many sea-going folk are not satisfied to merely understand
and use the remits of calculations given to them, but are
determined to know and understand the whole process of
calculation^ by means of which these results are obtained, and,
in consequence, very many hours have been spent in replying
to queries of this nature. It will be evident that, as we come
to deal with some of the more intricate calculations, a
moderate amount of mathematical knowledge is required.
However, it is hoped that by first dealing with the simple
preliminary calculations in Chapter X., and then following on
to the actual set of ship calculations, for which the necessary
drawings are given, together with brief notes and explanations
VI PREFACE.
of the various steps taken, the reader will be able to trace the
arithmetical application of the rules given.
Considerable additions have been made in Chapter III. on
the subject of water pressures, and in Chapter VI. (Section
III.) on, the subject of* waterballast, to illustrate which
numerous new diagrams have been inserted. Trim (Chapter
VII.) is entirely new, and, it is hoped, will meet the require-
ments of those readers at whose suggestions it has been intro-
duced. This chapter, in the form of a paper, was read before
the Shipmasters' Society in London, in March 1898, and the
request was there repeated that it should find a place in
Know Tour Own Ship.
The other sections of the book have been revised, and, as far
as possible, brought up to date.
Suggestions involving details of ship construction will be
fully dealt with in the companion volume, Construction
and Maintenance of Steel Ships, undertaken by the Author
at the special request of the publishers. -
In its enlarged and improved form, it is hoped that this
volume will meet with the same cordial acceptance which has
been the chief characteristic of its history during its three
years' existence.
* Extracted largely from a paper read by the Author before the Ship-
masters' Society, London, November, 1897.
London, Aprils 1899.
AUTHOR'S PREFACE TO THE
FIRST EDITION.
Experience is a wonderful teacher, though often a very slow
one. In the course of time, it will instil into a seaman's
mind a considerable knowledge of the capabilities and
behaviour of his vessel under varying circumstances — her
strength, her carrying capacity, her stability, or, in other
words, her sea qualities.
This mode of obtaining knowledge is, however, far too
costly for the intelligent seaman of to-day. He knows that
many a good ship, and what is worse, many precious lives
have been lost before it has been acquired, and all through
pure — though it would be unjust to say, wilful — ignorance.
As regards the subject of stability, it has been said that it
is useless to provide a captain with curves of stability, for he
does not understand them, and if he did, they are of little
use, all he requires being a statement of certain conditions of
loading, beyond which he must not go, or his vessel will be
unsafe. This is all very good in its way, but why does the
captain not understand curves of stability, or, more broadly
speaking, the subject of stability ? Is not the answer this,
that very little indeed has been done to provide the means of
his obtaining such important information? Besides, if the
curves are of little use, and a statement of conditions to
Vm PREFACE.
ensure safety is sufficient, some credit must be given to the
intelligence of the ship's officer of to-day. Let him not be
put down as a machine to. steer a ship, incapable of compre-
hending what may be reduced to a subject of comparative
simplicity. On the other hand, let it not be supposed that
lengthy experience in navigating ships necessarily means
capability to so load any ship as to produce seaworthiness.
The ignorance often displayed in loading and ballasting
vessels, and the loss resulting therefrom, prove that such is
not the case.
It is evidently often imagined that able, valuable, and in-
structive papers and lectures on vital subjects relating to
ships, are only for, and interesting to, naval architects and
experts, and that to ships' officers they are either unnecessary
or else they have no' interest in this means of instruction. A
more foolish and unjust conclusion could scarcely be arrived at.
If the stability of a vessel depends so much upon the loading,
and officers superintend the loading of their own vessels, at
any rate in foreign ports, if not always at home, the importance
of an intelligent knowledge of the subject must be evident.
Moreover, is it not a fact that, with this knowledge, the
ship's officer would be able to supply a great amount of
valuable data to the shipbuilder and naval architect concern-
ing the behaviour and capabilities of his vessel under every
condition of weather and loading, which could not fail to be
of immense value in the designing of future ships ? By this
means, the designer, who, as a rule, sees little of the ship he
designs after a few hours' trial trip, generally under the most
favourable circumstances, would then be the better able to
produce a vessel more perfectly adapted to her requirements.
That such is the case is proved by the fact that some leading
shipbuilding firms do everything in their power to encourage
PREFACE. IX
ship captains to give all the information they possibly can
regarding the behaviour and performance of the vessels which
they have built.
The best method of supplying this kind of instruction to
seamen is believed to be by means of lectures thoroughly
illustrated by diagrams and experiments.
During the past few years the writer has, in the Govern-
ment Navigation School, Leith, N.B., given courses of
lectures, specially designed for the instruction of seamen.
The eagerness and enthusiasm displayed to obtain such in-
formation made it manifest that seamen are fully awake to
its importance, and appreciate and understand its value. The
able discussion which often followed these lectures, and the
important points and features brought out in connection with
personal experience, furthermore proved that seamen want no
rule-of-thumb methods for guidance, but that a thorough grasp
of the principles of the subject is required. This, together
with the repeated requests which have been made to publish
these lectures, has tempted the writer to do so in the form of
this book. The old-fashioned method of "beginning at the
beginning " of the subject has been adopted as the only trust-
worthy way of dealing with it; and while endeavouring to
cover as much ground as possible, the aim has been to con-
dense - the matter as far as compatible with clearness, to
present it in language easy enough to be understood by every
seaman, and stripped of laborious mathematical formulae, and
at a cost which will place it within reach of seamen of limited
means.
It is felt that no apology is necessary in presenting this
book, for while the excellent work of Sir E. J. Eeed and also
that of Sir W. H. White are admirably adapted to the require-
ments of the naval architect and the shipbuilder, it is beUeved
X PRBFACB.
that no special attempt has been made to supply the need of
seamen generally.
It is further hoped that the chapters on Construction,
Tonnage, and Freeboard, while interesting and important
subjects to seamen, will make the book acceptable to the ship-
owner, ship superintendent, ship draughtsman, and to those
generally interested in shipping.
The Author's sincerest thanks are due to Messrs. W. Denny
& Brothers, Dumbarton ; to Messrs. J. L. Thompson & Sons,
Ltd., Sunderland ; and to Messrs. Eamage & Ferguson, Ltd.,
Leith, for permission to use curves of stability of vessels built
by them; and also to J. Bolam, Esq., Head Master of the
Government Navigation School, Leith, for the kindly sympathy
and interest which he has manifested in the preparation of
the book.
Suggestions and communications — especially from ships'
officers and others desirous of promoting this branch of
nautical instruction — will be gladly welcomed and acknow-
ledged in future editions of this work, should these be called
for.
Leith, March^ 1896.
EDITOR'S PREFATORY NOTE
This Series has been designed to meet the growing desire
on the part of Ofl&cers in the Mercantile Marme for a
MORE SCIENTIFIC INSIGHT into the principles of their pro-
fession, and the sciences upon which the Art of Navigation
is founded. The treatises are, for the most part, written
BY Sailors for Sailors; and, where this is not the case,
by authors who have special knowledge of the subjects
dealt with and their application to the Sailor's life. The
treatment will be thoroughly scientific, yet as free as pos-
sible from abstruse technicalities, and the style such as will
render it easy for the young sailor to gain a knowledge
of the elements of his profession by private reading and
without difficulty.
KB.
London, March, 1896.
CONTENTS.
Chapter I. — Displacement and Deadweight.
PAQES
Displacement — Displacement Carves — Deadweight — Deadweight
Scale — **Tons per Inch Immersion" — Examples of Practical
Application of "Tons per Inch Immersion" Curve — Coeffi-
cients of Displacement, 1-11
Chapter II. — Moments.
Moments — Examples of Moments — Centre of Gravity — Effect
upon Centre of Gravity of Moving Weights on a Ship,
Vertically and Transversely, . * 12-18
Chapter m. — Buoyancy.
Buoyancy — Water Pressures — Reserve Buoyancy — Sheer — Value
of Deck Erections — Centre of Buoyancy — Curves of Vertical
and Longitudinal Centres of Buoyancy — Eflfect upon a Ship's
Centre of Buoyancy of Immersing or Emerging Wedges of
Buoyancy — Effect of Entry of Water upon Buoyancy —
Camber, or Round of Beam — Testing Water Ballast Tanks, . 19-39
Chapter IV. — Strain.
Relation of Weight of Material in Structure to Strength — Strain
when Floating Light in Dock — Relation between Weight and
Buoyancy — Strain Increased or Decreased in Loading —
Distribution and Arrangement of Material in Structure, so
as to get Greatest Resistance to Bending — ^IVpes of Vessels
subject to Greatest Strain — Strains among Waves — Panting
Strains — Strains due to Propulsion by Steam and Wind —
Strains from Deck Cargoes and Permanent Weights— Strains
from Shipping Seas — Strains from Loading Cargoes Aground, . 40-60
XIV CONTENTS.
Chapter V.— Structure.
PAaES
Parts of Transverse Framing, and how Combined and United to
produce Greatest Resistance to Alteration in Form — Sections
of Material Used — Compensation for Dispensing with Hold
Beams — Parts of Longitudinal Framing, how Combined and
United to Transverse Framing to produce Greatest Resistance
to all Kinds of Longitudinal Bending and Twisting — Forms of
Keels and Centre Keelsons, and their Efficiency — Distribution
of Material to Counteract Strain — ^Value of Efficiently-worked
Shell and Deck Plating in Strengthening Ship Girder — Defini-
tions of Important Terms — Illustration of Growth of Struc-
tural Strength, with Increase of Dimensions, by means of
Progressive Midship Sections — Special Strengthening in
Machinery Space — Methods of Supporting Aft End of Shafts
in Twin-Screw Steamers — Arrangements to prevent Panting
— Special Strengthening for Deck Cargoes and Permanent
Deck Weights, and also to Counteract Strains due to
Propulsion by Wind — Types of Vessels — Comparison of
Scantlings of a Three-decked, a Spar-decked, and an Awning-
decked Vessel — Bulkheads — Rivets and Riveting, . . . 51-111
Chapter VI. (Section I.).— Stability.
Definition — The Righting Lever — The Metacentre — Righting
Moment of Stability — Conditions of Equilibrium — "Stiff"
and "Tender" — Metacentric Stability — Moment of Inertia
— Agents in Design influencing Metacentric Height — How to
obtain Stiffness — Changes in Metacentric Height during the
Operation of Loading — Stability of Objects of Cylindrical
Form — A Curve of Stability — Metacentric Curves — How the
Ship's Officer can Determine the Metacentric Height and
then the Position of the Centre of Gravity in any Condition
of Loading — Effect of Beam, Freeboard, Height of Centre of
Gravity above Top of Keel, and Metacentric Height upon
Stability — Wedges of Immersion and Emersion — Effect of
Tumble Home upon Stability — Stability in Different Types
of Vessels, 112-147
Chapter VI. (Section II.).— Rolling.
Rolling in Still Water — Relation of Stiffness and Tenderness to
Rapidity of Movements in Rolling — Resistances to Rolling —
Danger of Great Stiffness — Rolling among Waves — Lines of
Action of Buoyancy and Gravity — A Raft, a Cylinder, and
a Ship among Waves — Synchronism : how Produced and
Destroyed — Effect of Loaaing upon Behaviour — Effect of
Transverse Arrangement of Weights upon Rolling Motions —
Alteration in Behaviour during a Voyage — The Metacentric
Height — Fore and Aft Motions — Fore and Aft Arrangement
of Weights, 148-165
CONTENTS. XV
Chapter VL (Section ni.).— BaUasting.
PAGES
Similar Metacentric Heights at Diflferent Draughts — Wind
Pressure — Amount- and Arrangement of Ballast — ^Means to
Prevent Shifting of Ballast — Water Ballast — ^Trimming Tanks
— Inadaptability of Double Bottom Tanks alone to provide an
Efficient Means of Ballasting — Considerations upon the Height
of the Transverse Metacentre between the Light and Load
Draughts, and Effect upon Stability in Ballast— Unmanage-
ableness in Ballast — Minimum Draught in Ballast — Arrange-
ment of Ballast, 166-185
Chapter VI. (Section IV.)
Loading — Homogeneous Cargoes.
Alteration to Curve of Stability, owing to Change in Metacentric
Height— StabUity of Self-Trimming Vessels— Turret— Trunk, 186-192
Chapter VI. (Section V.). — Shifting Cargoes.
Variations in Stability on a Voyage, 193-197
Chapter VX (Section VX)
Effect of Aidmission of Water into the Interior of a Ship.
Admission through a Hole in the Skin into a Large Hold — Curves,
showing Variation in Height of Metacentre with Increase of
Draught — Buoyancy afforded by Cargo in Damaged Com-
partment — Longitudinal Bulkheads — Entry of Water into
Damaged Compartment betieath a Watertight Flat — Entry
of Water into Damaged Compartment beneath a Watertight
Flat — Value of Water Ports — Water on Deck — Entrance of
Water through a Deck Opening — Entry of Water into an
End Comjmrtment — Height of Bulkheads — Waterlogged
Vessels, 198-212
Chapter VX (Section Vn.)
Sailing— Sail Area, etc., 213-218
Chapter VI. (Section VHI.)
Stability Information, 219-221
Chapter VI. (Section IX.)
Closing.Remarks on Stability, 222-225
XVI
CONTENTS.
Chapter Vn. — Trim.
Definition — Moment to Alter Trim — Change of Trim — Centre of
Buoyancy of Successive Layers of Buoyancy at Successive
Draughts — Longitudinal Metacentre — Longitudinal Metacentric
Height — ^Moment to Alter Trim One Inch — Practical Examples
showing how the Change of Trim is Ascertained,
Chapter YUL —Tonnage.
Importance to Shipowners from an Economical Point of View —
Under-deck Tonnage — Gross Tonnage — Register Tonnage —
Deductions for Register Tonnage — Importance of Propelling
Deduction in Steamers — Deep Water Ballast Tanks — Deck
Cargoes — Examples of Actual Ship Tonnages — Sailing Vessels
— Suez Canal Tonnage — Yacht Tonnage, . . , • .
Chapter IX. — Freeboard.
Definition — Method of Computing Freeboard — Type of Vessel —
Nature of Deductions, and Additions to Freeboard — Examples
of Estimating Freeboard for Different Types of Vessels, .
Table of Natural Sines and Cotangents, etc.,
Chapter X. (Section I.). — Calculations.
Useful Tables and Rules — Calculation of Weight of Steel Plate —
Stanchion — Hollow Stanchion — Gallons in Fresh Water Tank
— Tons in Coal Bunker — Rectangular Barge's Displacement and
"Tons per Inch" Immersion — Simpson's Three Rules and
Graphic Explanations — Calculation of Area of Deck or Water-
plane — **Tons per Inch" Immersion of Ship's Waterplane —
Ship's Displacement — Centre of Gravity of a Waterplane, Longi-
tudinally or Transversely — Centre of Buoyancy, Vertically and
Longitudinally — Moment of Inertia — ^Transverse Metacentre
above Centre of Buoyancy — Centre of Gravity — Longitudinal
Metacentre above Centre of Buoyancy — Alteration of Trim —
Area of Section and Volume and Centre of Gravity of Wedge
of Immersion or Emersion — Centre of Effort, . . • .
PAOSS
226-238
239-250
251-267
268-270
271-300
Chapter X. (Section IL).
A Set of Ship Calculations as Worked from Actual Drawings.
Displacement — Longitudinal Centre of Buoyancy — Vertical Centre
of Buoyancy — Transverse Metacentre above Centre .of Buoy-
ancy, showing two Methods of Arrangement — Tons per Inch
Immersion — Wetted Surface and SheU Displacement — Longi-
tudinal Metacentre above Centre of Buoyancy — Results of
Calculations upon Curves— Stability Calculation, . . . 301-324
Appendix A : Dynamic Stability and Oscillations among Waves, . 325-328
Appendix B : Test Questions, 328-332
Index, 333
KJS^OW YOUE OWN SHIP.
CHAPTER I.
DISPLACEMENT AND DEADWEIGHT.
Contents. — Displacement — Displacement Curves — Deadweight — Dead-
weight Scale — **Tons per Inch Immersion" — Examples of Practical
Application of **Tons per Inch Immersion" Curve — Coeificients of
Displacement.
Terms. — " Displacement," " Deadweight," and " Tonnage " are
terms often heard and used by those associated with ships and
shipping in some form or other, but not always definitely under-
stood. Their simplicity, however, renders them easy of explana-
tion, and we shall, at the outset, devote our attention briefly
to the two former — Displacement and Deadweight. The last
— Tonnage — being a subject of larger dimensions, though simple
in its character — will be reserved for a later chapter.
Displacement. — ^Any object floating in water displaces or
dislodges a volume of water, and the weight of the displaced
water is equal to the weight of the floating object. The prefix
"dis " in the word "displacement" means ** away from." Thus,
displacement reveals its own meaning — viz., that which is placed
out of its usual condition.
Displacement, in the technical sense in which it is applied to
ships, or any other floating bodies, refers to the displacing of the
water by the total or partial immersion of any object placed in
it. The volume of water displaced may be measured in cubic
feet or in tons, and the weight of water displaced is called the
Displacement,
This fact may be simply illustrated by supposing a tank to be
A
KNOW YOUR OWN SHIP.
filled to the brim with water, and when in this condition let a
box-shaped ship— 3 feet long, 2 feet broad, and 2 feet deep-
be placed in it, sinking to a depth of 1 foot. It is evident that
if the tank were full before the ship was placed in it, some of
the water must have overflowed (fig. 1).
Let a receiver be placed below the tank, with a reservoir
3 feet long, 2 feet broad, and 1 foot deep (exactly the same
dimensions as the immersed part of the ship), attached to the
bottom. It would be found that immediately the overflow had
ceased, the reservoir would be just filled as shown by the dotteri
lines. This proves that the volume of water displaced is exac>iy
J
&.0 f
"■^^
zr~'C'zz
< 1
1
— —
— — — — — _
Z.1
— — — — — ^ — — —
\
"1
■bzstolts:-
1
Fig. 1. — Displacement.
equal to the volume of the immersed portion of the ship. More-
over, if the ship could be placed in one balance, and the dis-
placed water in another, they would be found to exactly equal
each other in weight. But supposing the ship were too large
for any process of weighing to be adopted, the displacement
could be ascertained by a very simple calculation.
A cubic foot of sea water weighs 64 lbs., and 35 cubic feet of sea water
weigh 1 ton. Multiply together the length, breadth, and draught of the
ship, and we get cubic feet ; 3x2x1 = 6 cubic feet. Therefore, since
1 cubic foot weighs 64 lbs., 6 cubic feet will equal 6 x 64 = 384 lbs. dis-
})lacement, and this, while being the weight of water in the reservoir, is also
the total weight of the ship in its present condition.
Again, sui)posing an unknown weight be placed in the ship increasing
DISPLACEMENT AND DEADWEIGHT. 3
the draught to 1 foot 6 inches, or 1*5 feet, then 3x2x1 -5 = 9 cubic feet,
9 X 64 = 676 lbs. total displacement.
The displacement, when the ship was empty, was 384 lbs., therefore the
weight added is 576 - 384 = 192 lbs.
In dealing with floating objects not box-shaped, such as real
ships, although the same method of computing the displacement
.scAue or tons
JOO ^00 SCO AOO
500 fioo
Fig. 2.— Displacement Cueve.
cannot be adopted owing to the difference in form, yet the
principle, that the weight of water displaced equals the total
weight of the ship, remains the same. This important fact, as is
evident, proves of immense value to shipbuilder and shipowner
alike, for had the weight of a ship to be found by estimating
the weight of every item in it — hull, engines, boilers, masts, etc.
— separately, and adding them together, it will be seen how
4 KNOW YOUR OWN SHIP.
laborious the process, and how inaccurate the result, might
possibly be.
The length, breadth, and draught of a ship cannot be multi-
plied together for displacement, but, by the application of a
simple method known as Simpson's rules, the volume of the
immersed portion of the ship can be ascertained, which, if con-
sidered as water, and divided by 35, will give the displacement
in tons. (See Chapter X. for Simpson's Rules and Calculations.)
To make a separate calculation whenever the displacement
is required at any particular draught would entail considerable
labour and inconvenience. This is avoided by using what is
termed a Displacement Curve, by means of which, in a moment,
the displacement can be read off at any draught. It is con-
structed in the following manner (fig. 2).
Draw the vertical line A B, and upon it construct a scale at,
say, J inch = l foot, indicating the draughts up to the load line,
exactly as read upon the stem or stem of a vessel, inserting in
each foot space twelve equal divisions for inches. From the top
of the line A B draw the horizontal line A C. Divide this line
into ^-inch spaces, each one representing 100 tons of displace-
ment. Subdivide the spaces again into tenths, each of which
will, therefore, represent 10 tons. Supposing our vessel be of
box form, 100 feet long, 20 feet broad, and 10 feet draught, then
by calculating the displacement at a series of draughts, say 2,
4, 6, 8, and 10 feet respectively, we are in a position to find a
number of points by means of which the displacement curve is
constructed.
The displacement at —
2 feet draught = 100 x 20 x 2 = 4,000 cubic feet
4^-114-2 tons.
35
4 feet draught = 100 x 20 x 4 = 8,000 cubic feet
?i^0-228-5tons.
35
6 feet draught = 100 x 20 x 6 - 12,000 cubic feet
lM2?=342-8 tons.
35
8 feet draught - 100 x 20 x 8 = 16,000 cubic feet
1^^=457-1 tons.
35
10 feet draught = 100 x 20 xlO = 20,000 cubic feet
' 20,000
35
To construct the curve proceed as follows : —
=571 "4 tons.
DiapLACBMHKT AND DEADWBlGHT. 5
KNOW YOUR OWN SHIP.
Through the 2, 4, 6, 8, and 10 feet draughts on the scale
draw lines parallel to the line AC. The displacement at the
2 feet waterline is found to be 114*2 tons. Through the point
in the horizontal scale of tons representing this, drop a vertical
line to the 2 feet waterline. The intersection of these lines
gives the first point in the curve. Repeat the same operation
for the other displacements at their respective waterlines. A
line through the points of intersection gives the displacement
curve. For a box-shaped vessel, it is a straight line as shown.
Having this, the displacement can be read off at any inter-
mediate waterline between the bottom of the keel and the load
waterline. The displacement curve for an actual ship is con-
structed in the same way. Fig. 3 is an illustration of such an
one.
The load waterline in this case is 14 feet above the bottom of
the keel, which .indicates on the curve 1400 tons of displacement.
The mean draught of the vessel in her light condition is 7 feet,
which reads from the curve 550 tons displacement, leaving a
carrying capacity or deadweight of (1400-550 = ) 850 tons.
Let these terms be clearly understood. Tlie total weight of the
ship in whatever condition and floating at any draught is equal to
the displacement at that draught, Deadioeight is carrying power
only^ over and above the actual weight of the ship and her
equipment. It, therefore, comprises cargo and bunker coal.
The deadweight of a ship floating at a particular draught is the
difference between tJie displacements in the light condition, and at
that draught.
From the displacement curve an even simpler method of
indicating displacement can be arranged, useful more especially
to the officer of the cargo-carrying vessel. This is a Vertical
Displacement Scale, and with it is usually combined a Deadweight
Scale (see fig. 4).
Column 2 is a scale of draughts exactly similar to the scale
of draughts on the displacement curve. Column 1 is a scale
indicating the displacements corresponding to the draughts, the
readings of which are identical with the readings from the curve,
since the one is constructed from the other. For example, strike
a horizontal line AB from the displacement curve to the ver-
tical scale at, say, 8 •feet draught. The reading from the curve
gives 655 tons, which is the same on the vertical scale.
. Column 3 is a deadweight scale. As already pointed out,
deadweight is the difference between tbe displacement at any
particular draught and the weight or the displacement of the
vessel when light. In the above case the vessel floated light at
a mean draught of 7 feet, which represents 550 tons on the
DISPLACEMENT AND DEADWEIGHT. 7
displacement scale, while tlie deadweight stands at nil. The
difference between the displacements at light draught and at 1
foot intervals above the light draught will equal the respective
deadweights at these draughts.
Column 4 represents the freeboard. More about this will be
found in Chapter IX. Suffice it for the present to state that
by freeboard is meant the distance from the top of the weather
decks at midships to the waterline at which the vessel floats.
It is, therefore, measured from the deck downwards. In the
above case the minimum freeboard was fixed at 2 feet.
Thus, by means of the vertical scale, a ship's officer can read
at a glance the total displacement — the deadweight and the
corresponding freeboard — at any particular draught.
Tons per Inch Immersion. — Another very useful curve,
closely related to the subject of displacement, may be constructed.
This is known as the Tons per Inch Curve, By " tons per inch "
is meant the number of tons necessary to be placed on board or to
be taken out of a vessel, to effect an increase or decrease of 1 inch
in the mean draught. Thus the term " tons per inch " really
means displacement per inch. It is found by calculating the
displacement for a foot of the depth at the particular draught at
■which the vessel is floating, and dividing this by 12. The result
is the increase or decrease of the displacement for 1 inch altera-
tion in draught, or " tons per inch."
The area of the waterline in square feet is first found, and
reckoning this to be a foot deep, the square feet are at onco
converted into cubic feet. These cubic feet divided by 35 give
the number of tons per foot. Tons per foot divided by 12 give
the required " tons per inch."
The formula may be written thus : —
Area of waterline _ Area of waterline _ <, ^^^^ .^^. „
35 X 12 "" 420 * ^*
The "tons per inch" for the box vessel, for which the dis-
placement curve (fig. 2) was constructed, w^ould be : —
100 X 20 = 2000 square feet area of waterline. .
2000 X 1 = 2000 cubic feet of displacement.
?2?2=47 "tons per inch."
420 ^
It will be observed that since a box vessel is unchanging in
horizontal section from the bottom to the top, the "tons per
inch" will be the same at any draught, thus rendering the
construction of a curve unnecessary. This is not so in the case
of an ordinary ship. The waterplanes, from the top of the keel
8
KNOW YOUR OWN SHIP,
8CAl.eOPTONS
to the load waterline, all varying in form, necessitate the con-
struction of a curve for readiness and convenience, so that the
" tons per inch " may be ascertained immediately for any draught.
This curve is made in the same manner as the displacement
curve. The " tons per inch *' at the 4, 8, 12, and 16 feet heights
above the top of the keel are 8'4, 9*7, 10*36, and 10*6 respec-
tively. Vertical lines are dropped from these positions on the
"tons" scale to their respective waterlines, the intersections of
which give the points necessary for the construction of the curve
(fig. 5). Its shape is somewhat different from the displacement
curve for this reason. With every increase of draught the
displacement must increase, and especially in the region of the
load waterline, where the vessel
is fullest in all ordinarily de-
signed vessels, thus tending to
make the curve continue to
spread. On the other hand,
the "tons per inch" increases
rapidly until the vicinity of the
load waterline is reached, and
then the sides of the vessel,
in the case of ordinary cargo
steamers, being somewhat per-
pendicular, there is little varia-
tion in the area of the water-
planes, and here the " tons per
inch" remains about the same, the
curve contracting and bending
to a vertical position, as shown
in the illustration. As an ex-
ample of how to read the " tons
per inch " curve at, say, 6 feet
6 inches draught, strike the
horizontal line AB to the curve. At the point of intersection
draw a vertical line to the scale of tons, and there is indicated 9*1
" tons per inch."
The use of a curve of " tons per inch" may be illustrated in a
variety of ways.
For example, suppose a vessel to be floating at a certain
draught, at which the "tons per inch" is 15. On calling at a
port a moderate quantity of cargo has to be discharged, the
weight of which is not exactly known. After discharging, the
mean draught is found to have decreased 4J inches, therefore
the weight of the cargo discharged is 15 x 4J = 67 J tons.
Again, supposing a steamer floating at her load waterline, where
Fig. 5. — "Tons per Inch" Curve.
DISPLACEMENT AND DEADWEIGHT. 9
the " tons per inch " is 15, to consume 100 tons of coal on a
voyage, the decrease in draught would be -— - = 6*6 inches
ID
approximately. Every seaman knows that on a vessel psissing
from salt to fresh water, an increase occurs in the mean draught,
and a decrease when passing from fresh to salt water. The
reason for this is, that salt and fresh water differ in density,
and thus present different supporting qualities to objects floating
in them. To support 1 ton of weight requires a displacement of
36 cubic feet of fresh water, while salt water, being denser and
heavier, and more capable of affording support, will bear up a
weight of 1 ton on a displacement of 35 cubic feet.
Sometimes where the depth of entrance to a dock is limited,
it is very necessary to know what change of draught will occur
in passing from salt to fresh water, or vice versd. At the load
draught this is marked on the ship's side by the Board of Trade,
or one or other of the Registration Societies, if the vessel is
classed. By the aid of the ** tons per inch " curve, we may
ascertain the change in draught for ourselves. Suppose a vessel
to be floating at a certain draught where the displacement is
4,500 tons, and the " tons per inch " 20. Now, a cubic foot of
sea water weighs 64 lbs., and a cubic foot of river water, which
is chiefly fresh, about 63 lbs., the difference being -^j* Since
the total weight of the ship remains the same, the total weight
of water displaced must remain the same also, though as it
becomes fresh water it increases in volume, because it is ^^^
lighter, measure for measure. As already stated, when floating
in sea water, she displaces 4500 tons. Suppose her now to be
floating in river water at the same waterline, her weight or
displacement will be -^^ less.
,V of 4500 = 70*3 tons*
The "tons per inch'* was 20 tons in salt water, but it also
will be ^ less.
20 X — = 191 J ** tons per inch " in river water.
64
The change in draught will therefore be —
70-3 -r 191i = 3-57 inches.
* Fresh water may be taken at 62i lbs. per cubic foot.
10
KNOW YOUR OWN SHIP
The formula may be shortened, and written thus —
s
pj of displacement -i- -;- ol " tous per inch" = increase in draught;
therefore,
4500
63 x20
= 3*57 inches.
Coefficients of Displacement. — In comparing the displace-
ment or underwater form of one vessel with another, it is not
sufficient to say that one is long and the other short, one broad
and the other narrow, or one deep and the other shallow. Nor
is a numerically correct idea conveyed by saying that one is fine
and the other full or bluff. A more comprehensive means must
be adopted, and this is attained by coefficients.
Suppose that out of a block of wood 6 feet long, 1|- feet broad,
and 1 foot deep, the model of the underwater form of a vessel
6 -O
Fig. 6.— Model of Underwater Form.
■H
be cut out, as shown by fig. 6, the extreme dimensions of which
are — length, 6 feet ; breadth, 1^ feet ; depth, 1 foot.
Before the block was cut, it contained 6x1^x1=9 cubic
feet. The extreme dimensions of the remaining part in the
form of the model are still the same — 6 feet long, 1^ feet broad,
1 foot deep — but much of the volume of the block has been cut
away, as shown by the hatched lines, leaving, say, 6 cubic feet,
6 2
which is -— == -^ , or, as it is generally written, '66 of the whole
block, and this is termed the coefficient^ or, in other words, the
t
DISPLACEMENT AND DEADWEIGHT. 11
comparison of fineness. Thus the coeflBcient of fineness of any
vessel is the fractional part (usually expressed in decimals) which
the volume of the displacement bears to the circumscribed block.
•8 would be a very full vessel.
"7 to 75, an average cargo steamer.
•65, a moderately tine cargo steamer,
•6, a fine passenger steamer.
•5, an exceedingly fine steamer, but an average for steam yachts.
'4, a very fine steam yacht.
By means of coefficients a comparison of the displacement or
fineness between two or more vessels may be struck relatively to
their circumscribing rectangular blocks.
Vessels of the same extreme dimensions, and the same co-
efficients of fineness, and, therefore, the same displacements, may
vary considerably in form or design, which in turn may affect
the speed.
Knowing the extreme dimensions of a vessel, and the coefficient
of fineness, the exact displacement can easily be arrived at. For
example, take a vessel 100 feet long, 20 feet broad, and floating at
8 feet draught, the coefficient of fineness being -6.
The displacement would be —
l£5Jli2jUjLJ„ 27^.2 tons.
12 KNOW YOUR OWN SHIP.
CHAPTER 11.
MOMENTS.
Contents. — Moments— Examples of Moments — Centre of Gravity — Effect
upon Centre of Gravity of Moving Weights on a Ship, Vertically and
Transversely.
Moments. — Moment of a Force about a Point. — We may
speak of a ship when inclined from the. upright position as having
a moment tending to bring her to the upriglit position again.
This is usually termed a righting moment. On the other hand, it
might be found that when the vessel was inclined to a certain
angle, she possessed no inclination to return to her original upright
position, but continued to heel until she capsized. In this case,
we may say she possesses an upsetting^ or capsizing moment.
This important term " moment " is easily understood. Every-
body knows the meaning of simple distances like inches and
feet, and of simple weights like pounds and tons. We must
accustom ourselves to quantities which are got by multiplying
distances by weights. Thus, we may have to multiply 5 feet
by 8 tons. The product is called 40 foot-tons. If we multiply
5 feet by 8 pounds, the product is called 40 foot-2^otmds. If we
multiply 5 inches by 8 tons, the product is called 40 inch-tons.
Now weight is one kind of force, and other forces, such as
pressures and resistances (say, wind or steam ' pressure and water
resistance), are also conveniently measured in pounds or tons.
And pounds or tons of any kind of force, such as pressure and
resistance, may also be multiplied by inches or feet of distance,
giving inch-tons, or foot-pounds, etc., as the case may be.
Now the quantity called the Moment of a Force (the only
kind of moment we want just now) is got by taking some weight
or other force and multiplying it hj what may be conveniently
called its leverage. This leverage is the perpendicular distance of
the direction in which the force acts from some conveniently
chosen point. The point often chosen for this purpose in a ship
is the centre of gravity of the ship. For instance, 5 tons of wind
pressure on sails multiplied by a leverage from the ship's centre
of gravity of 30 feet would give a moment of force about that
centre of gravity of 5 x 30 = 150 foot-tons. And a water pressure of
1000 tons multiplied by a leverage from the same centre of gravity
MOMENTS, 13
of 3 inches would give a moment of force about that centre of
gravity of 1000 x 3 = 3000 inch-tons.
Simple illustrations of moments of force may be got from
levers.
Let AB (fig. 7) be a lever 5 feet long, supported at one
end, A, as shown, and at the other having a weight of 4 tons
suspended at right angles to the lever. In this condition there
is a moment about A of 4x5 (weight multiplied by distance
from centre of weight to point of support) = 20 foot-tons, tending
to capsize, or break, or bend the lever at the point A, and the
20 foot-tons in this case may be called a capsizing moment,
Fig. 7. — ^Weight Acting on a Lever.
or a bending moment. Let the lever be subdivided into foot
intervals at the points C D E F. If the weight be now moved
to the point F, which is 4 feet from A, the moment about A will
be 4x4 = 16 foot-tons. In like manner, if moved
To the point E, the moment about A will be 4 x 3 = 12 foot-tons.
D, „ » 4x2=8 „
,, ^i ti i> 4x1 — 4 ,,
„ A, „ „ 4x0=0,,
The last, no foot- tons, as will be seen, is accounted for by the
fact that the downward force of weight is acting in the same
vertical line as the upward support, there being therefore no
capsizing moment ; or, as we are speaking of a lever or bar, no
breaking or bending moment.
There is just another point bearing on moments which will
also assist us in studying the structure and strains of ships.
In most cases the leverage is the variable factor in influencing
the amount of foot-tons, the weight remaining constant. It
should now be noticed tiiat the moment is alivays greatest at the
point of support, and when the loeight is removed farthest from it.
Keeping the weight in the position shown at B, the tendency
to fracture at. the point C will be considerably less since the
leverage is less. The moment at this point is 4x4 = 16 foot-
14r KNOW YOUR OWN SHIP.
tons, and it will continue to diminish until, at the point B, it
has vanished completely.
But let us take another simple example illustrative of
moments. Fig. 8 represents a lever supported at the point A,
and with weights of 3 and 4 tons suspended at its extremities,
at distances of 8 and 5 feet respectively from the point of
support. First, what would be the tendency to fracture at the
point A ? On the side towards B there would be a moment of
£
Fig. 8. — Action of Weights on a Point of SuppopwT.
3 X 8 = 24 foot-tons, and on the side towards C, 4 x 5 = 20
foot-tons.
But suppose it is asked, "Is there a capsizing moment, and,
if so, how much ? " As we have already seen, there is a moment
of 20 foot-tons on the side towards C and 24 foot-tons towards
B, and since the moment towards B preponderates by 24-20 = 4
foot- tons, the lever would therefore capsize towards that side.
Centre of Gravity. — But suppose we wished to find the
point to which the support must be moved in order that the
moments might balance one another, the lever remaining in a
state of equilibrium or rest. This would be done by dividing
the difference of the two moments, which was found to be 4, by
the total weight 3 -h 4 = 7, 4 divided by 7 = 4- foot, and moving
the support this distance towards B, the side possessing the
greater moment. Let us prove this. The support, according
to our calculation, will now be 8-f = 7|- feet from B, and
5 + 4 = S-f feet from C.
Towards B the moment is now 3 x 7^ — 22f foot-tons.
„ G „ 4 X 5f - 22f „
Being exactly equal to each other, the lever remains at rest.
Now this halancing point or centre of moments is a very important
point. For the point at which a body (acted on only by its own
weight) will balance is called the centre of gravity of that body.
And the point at which a system of bodies (acted on only by
their own weight) will balance is called the centre of gravity of
HOMEXTS. 15
that sydem of bodies. An example of a system of bodies is a
ship with or without cargo in her. And as such a body as a
ship cannot be balanced experimentally so as to find the centre
of gravity by trial, the calculation of the moments in question
is employed upon the ship and the weights in her until their
balancing point is found, and that balancing point is the centre
of gravity of the ship and the load then in her, aud the whole
weight of ship and cargo may be supposed to act vertically
downwards through that point.
For, proceeding further, in ^g, 9, A B is a lever, with a weight
of 2 tons at a distance of 2 feet from the support, and a weight
of 4 tons at a distance of 4 feet from the support, both on the
same side, and, similarly, weights of 2 and 4 tons at 2 and 4 feet
respectively on the other side of the support. Then the moments
must be the same, and it is evident that the lever is supported
A B
B^
"S ^
3 i
:
Fio. 9. — Centee of Gravity.
at the centre of gravity of the total weight. Let a weight of
3 tons be now suspended from the extremity of the lever at li,
and at a distance of 6 feet from the support, as shown by the
dotted square. It is required to find the centre of gravity now.
Since the moments preponderate towards B by 3x6 = 18 foot-
tons, if this be divided by the sum of the weights, we shall get the
distance the centre of gravity has moved, which is j-lsslj^ feet
towards B.
But suppose that instead of a weight being added, the 2 ton
weight on the side towards B be removed. Let us find the centro
of gravity now. The moment towards A will preponderate by
2x2 = 4 foot-tons, and this, divided by the total weight, which
is 2 + 4 + 4 = 1 0, will equal -^ = f foot = shift of centre of
gravity towards A.
The reader is advised to make himself thoroughly familiar
with the principle of moments, as illustrated in this chapter, as
this will be found to be absolutely essential in order to deal
successfully with the following chapters. Whenever several
weights are connected by any means, as shown in the foregoing
examples, the combined system of weights acts directly through
16
KNOW YOUR OWN SHIP.
one balancing point, and this is their Common Centre of Gravity.
And, if this method of finding the common centre of gravity of
a ship and its load be used, one first finds how far from stem or
stem that centre of gravity lies, and how much it is shifted fore
or aft by shifting weights fore and aft. And precisely the same
sort of calculation may be used to find how far above the keel
the same centre of gravity lies, and how much up and down it
is shifted by shifting weights up and down in the ship. We
have only in this case to measure our leverages vertically above
and below the balancing point we are trying to find by assuming
a point for its position, and multiply the weights by the vertical
leverages to get the moments. We, therefore, now proceed to
show how to apply these principles to actual ships.
Effect of Moving Weights on a Ship's Centre of Gravity.
— Suppose a vessel be floating with her centre of gravity at the
Fig. 10.— Centre of Gravity of a Ship.
point G (fig. 10). (It may be said here that the position of
the centre of gravity of the ship when light could be supplied
by the builder, and this would limit the duty of the shipmaster
to finding the position of the centre of gravity with various
kinds of loading. But as it is not customary with all ship-
builders to do this, a simple experiment by which the shipmaster
himself may find the centre of gravity will be given later on.)
Her total displacement — that is, her weight — is 1000 tons. Let
a weight of 30 tons, already on board, be raised from the hold
and placed on the deck, at a distance of 20 feet from its former
position, as shown. What effect will this have upon the centre
of gravity ? Since the centre of gravity is in the centre of the
total weight it is evident that, if a tceight he raised, the centre
of gravity must travel in the direction of the mx)ved weight To
find the exact distance the centre of gravity has moved, the
MOMENTS. 17
same rule is adopted as in the case of a vertical lever. Multiply
tlie weight moved hj the distance it is moved, and divide the result
by the total weight or displacement,
1000 lUOO
the distance the centre of gravity has been raised.
Again, suppose the weight, instead of being placed on deck,
had been taken out of the vessel altogether. In this case,
multiply the loeight by its given distance from tlie centre of gravity
of the shipf say, 10 feet, and divide by tlie total displacement after
the weight is removed (1000 — 30 = 970 tons = displacement
after weight is removed),
s^^^Q » §22 - -3 foot,
970 970 '
the distance the centre of gravity has been raised.
Again, suppose, when the displacement is 1000 tons, a weight
of 30 tons be placed on board 10 feet below the centre of gravity.
Multiply the new weight by its distance from the centre of gravity^
and divide by the new displacement (1000 + 30 = 1030 tons = new
total displacement).
30_>^10 „ 300^ . -28 foot,
1030 1030 '
the distance the centre of gravity has been lowered.
Stakboard.
/
Fig. 11.— Effect of Weight Moved Athwartships.
Let us now notice the effect of a weight moved athwartships
(fig- 11).
B
18 KNOW YOUR OWN SHIP.
The centre of gravity is in the position shown at G, and the
total displacement is 1000 tons.
A weight of 20 tons already on board, on the centre of the
upper deck, is moved 10 feet to starboard. The centre of gravity
must move in the same direction, and in a line parallel to the
line joining the centres of the weight in its original, and in its
new position. To find the exact distance moved, rmiltiply the
weight by the distance moved, and divide by the total displacement,
_20j^l0 _ ^ ^ .2 foot.
1000 1000
(G G^), the distance the centre of gravity has travelled to
starboard.
BDOTAKCT.
CHAPTER III.
BUOYANCY.
COKTESTB. — Buoyancy — Water Pressores — Beserve Buoyancy — Sheer — Valae
of Deck Erections — Centre of Bnoyaney — Curves of Vertical and Longi-
tudinal Centres of Buoyancy — Effect upon a Ship's Centre of Buoyancy
of Imineraing or EmergiDR Wedges of Buovancy — Effect of Entry of
Water uoon Buoyancy — Camber, ot Bouna of Beam — Testing Water
Ballast I'aaks.
Buoyancy,- — Buoyancy means floating power. Under what
conditions will a vesBel float t Simply when its enclosed water-
tight volume is greater than its total weight in tons multiplied by
35, since it requires that 35 cubic feet of salt water bo displaced
before suflicient support is obtained to bear up 1 ton of weight.
If the enclosed watertight volume of the vessel in cubic feet is less
than its total weight in tons multiplied by 35, it will be evident
that the vessel will sink. This we have learned from the chapter
on "Displacement." But it may be aeked, "Why does a vessel
float 1" or "What is the nature of the application of the pressure
which is obviously produced by the water itself in order to sustain
an object of greater or less weight floating upon it?" This we
shall endeavour to explain.
FlO. 12, — iLmsTBATIKO Wateh Suppokt,
"Water Pressure. — Fig, 12 represents a tank nearly full of
fresh water. At the left-hand end of this tank is a hollow
20 KNOW YOUR OWN SHIP.
cylinder made of, say, sheet iron. It is completely watertight,
being entirely closed at the ends, one of which is a water-
tight lid. By ordinary calculation, its volume is found to be 1
cubic foot, the area of one end being 1 square foot and the height
1 foot. When totally empty, with the ends closed, its weight is,
say, 12 J lbs. A flat piece of sheet iron, similar to that from
which this cylinder is made, would sink if thrown into the tank,
while the sheet iron cylinder shows no signs whatever of sinking,
but floats as shown, with more than three-fourths of its volume out
of water. In order to immerse this tank so that its uppermost
surface is level with the water surface, there would require to be
an application of considerable downward pressure, which pressure,
if measured, would be found to be equal to a weight of 50 lbs.
(See second position of cylinder.)
Or, supposing that, instead of a downward pressure applied to
the outside, a weight of 50 lbs. had been placed inside the
cylinder, and the whole suspended on a spring balance, the total
weight registered will be 12J + 50 = 62J lbs. Suspended in mid
air, it is clear that the entire support is afforded by the spring
balance. While thus suspended, let the cylinder be gradually
lowered into the water in the tank. (See third position of
cylinder.) Immediately the bottom of the ' cylinder enters the
water, and the immersion increases, the spring balance registers a
reduction in weight, and this reduction continues in exact propor-
tion to the rate of immersion, until, by the time that the cylinder
is half immersed, it registers 31 J tons, and finally, when the
uppermost surface is flush with the water surface, the balance
registers 0, and the cylinder is barely maintained at the water
surface. The addition of the slightest weight would send the
cylinder to the bottom. Such an experiment as this, proves that,
while a floating object is subject to the same gravitation forces out
of the water as in it, the downward pressure of its weight is
balanced by an exactly equal upward pressure from the water
itself. Now, these upward water pressures are of enormous
importance to a floating ship, for not only, as we have seen, do
they aftbrd the support which keeps her on the bosom of the
ocean, but are the means whereby, when she is forcibly inclined
to a greater or less degree from the upright, she is enabled to
regain her normal position, though, under other conditions, these
same pressures may be the agents tending to capsize her when so
inclined. (The stability aspect of the subject is dealt with in
Chapter VI.). The foregoing experiment also enables us to
estimate the nature of the application of the upward water
pressures, for the spring balance clearly indicated that the
amount of this pressure varies directly as the depth.
BUOYANCY.
21
Thus, taking a rectangular object floating in salt water, as
shown in fig. 13, it can be similarly demonstrated that, for
every square foot of area on the bottom of the box, there is an
Surface
Upwmrd buoyant
presmure per
Mtfumrm faot
Fig. 13. — Illusteating Water Pressure increasing in Proportion
TO Draught.
upward pressure of 64 lbs. at 1 foot depth ; at 2 feet depth
the pressure is twice 64 lbs., and so on, in proportion to the
depth. An attempt has been made to illustrate this by drawing
the lines indicating the water pressures
denser as the depth increases.
Our next step is to ascertain the direction
of the application of these water pressures.
Take a vessel similar to that shown in
fig. 14, whose sides are perforated with
a considerable number of small holes. The
vessel is filled with water, and it is found
that from every hole the water squirts out
in a direction sqjuare to the surface of the
vessel, as shown.
Or take the same" vessel empty, and
plunge it into the water. Here, again, the
water is seen to squirt into the inside of the
vessel in a direction perpendicular to the
surface of the vessel. From these two illus-
trations it is evident that water contained in
a vessel, large or small, exerts its pressure
upon every unit of area on the inside, in lines
of action perpendicular to the surface. On
the other hand, when it is immersed, the
pressure on its immersed surface is also perpendicular to that surface.
So far, both by observation and the foregoing experiments, we
have arrived at the conclusion that a floating object, whether it
be the cylinder or a log of wood, or a 20,000 ton ship, is sup-
ported, or enabled to float by upward pressure given by the water
Fig. 14.— Water
Pressure.
22 KNOW TOUB OWN SHIP.
itself, and, moreover, that the water pressure is exerted in lines of
force perpendicular to the surface immersed — longitudinally, trans-
versely, obliquely, and verticaDy, as shown by the lines of water
pressures in fig. 15, tending to crush in the sides, ends, and bottom,
or to push the vessel out of the water. This is understood all the
move clearly when it is remembered that, immediately any floating
object is taken out of the water, the water rushes in on all sides.
Fia. IS.— Showing Lines op Watee pBEasuRE,
Volume Immerseci - buorancy. Volume above water level = reserve buoyancy.
and, more quickly than can be seen, the cavity formerly occupied
by the object is tilled, and the water is again at its uniform level.
Thus, while a ship is floating, the water has still the inclination,
if the phrase may be so used, to occupy the space filled by the
immersed volume of the vessel. Why the water does not succeed
in crushing in the esterior of the vessel wil! be dealt with in
another chapter on " structure." Why it docs not succeed in
thrusting the ship out of the water has already been explained by
the fact that there is the downward pressure of the weightof the
^ip itselt Thus a vessel will sink to a draught such that the
BCOTASCT.
23
reight
Bum of the upward preasores of buovancy eiactJy eqaal the n
of the ship. To balance & ship weighing, say, 500O tons, in mia
air, by means of sapports, such a^ pillars of iron, would be no easy
matter, A ship is a large, bulky object, and with such an
enormous weight, a rery careful estimate of the strength of the
supports and their positions would have to be made in order to
ensure the necessary couditiooa being fulfilled. But in water, the
support and balance are perfect. There are eiactly 5000 tons of
supporting pressurea from the water to exactly support the 5000
tons weight of the ship, and the balance ia perfectly effected bj- the
centre of the support (or the resultant of all tlie upward
pressures), and the centre of the weight being exactly in the
same vertical line, which condition is absolutely essential iu order to
preserve an esact balance : or, in other words, the centre through
which the resultant of the buoyancy pressures is exerted (B, tig. ID),
which is found to occupy a position in the centre of the displace-
ment or immersed volume, and the centre of gravity (G) mtist be in
the some vertical line iu order to ensure a condition of e<juiiibriiim.
24 KNOW TOUR OWN SHIP.
The net result is that, in a ship floating at rest, whether upright or
inclined, we have two equal opposing forces, exactly neutrsdising
each other, and therefore producing no motion whatever.
Figure 16 shows the same vessel, forcibly inclined, and, as
a result, the lines of force of gravity and buoyancy are no longer
exerted in direct opposition to each other, G being in exactly the
same position in the ship, while B has moved into the centre of
the immersed volume. A ship, or any floating object, on being
launched, or by any means placed in water, immediately, by these
natural laws, places herself in such a position as we have described ;
indeed, she must do so before a condition of rest can be main-
tained. Such a position is not necessarily the upright, considered
either transversely or longitudinally, but, under certain cir-
cumstances, due to form and the distribution of weight
constituting the ship and cargo, may necessitate the vessel
inclining to port or starboard, or trimming by the stem or the
stern. While the total buoyancy pressures and weight of a
floating ship are equal to each other, it must not be imagined
that these buoyancy pressures measure the total pressure upon
the immersed hull of a ship.
Fig. 17.— Showing the Total Pressure on the Immersed Hull
OF A Ship.
Figure 17 shows a box vessel floating, partially immersed.
The lines of water pressures are shown vertical on the bottom and
horizontal on the sides and ends (perpendicular to immersed surface).
The horizontal pressures afford no support whatever, simply
tending to push the vessel in the direction of their thrust. This,
however, is balanced by the opposing pressures on the opposite
side. The vertical surfaces of floating objects are exposed only to
horizontal, crushing pressures ; such surfaces only as are horizontal
or oblique are exposed to buoyancy pressures. So that a ship's
immersed surface endures all the upward pressures providing
buoyancy, or floating power, equal in amount, therefore, to her
own weight, and all the horizontal pressures in addition, which
afford no buoyancy, but simply tend to crush in the sides and ends
of the vessel. It is clear, then, that to estimate the amount of
buoyancy or upward pressure by using the total area of immersed
surface would be entirely wrong. It must be distinctly under-
BUOYANCY. 25
stood that only upward pressures, either vertical or oblique, afford
support, all others producing only crushing strains upon the
vessel's immersed exterior.
Remembering that supporting pressures increase in proportion
to the depth, a difficulty sometimes arises in understanding the
nature of the pressures in wholly immersed objects. For it is
reasoned that, if it be true that upward pressures increase with
depth, how comes it that, as soon as a vessel becomes too heavy to
remain supported at the surface of the water, it never finds a place
of rest until it reaches the bottom? The answer is simple
enough. It is quite true that, as the object descends in sinking,
the pressure on the bottom surface increases in direct proportion
to the depth, and remembering that water pressures are always
perpendicular to the immersed surface, the pressures on the upper
surface of the sinking object also increase in direct proportion to the
depth. Thus, while it is perfectly true that, as the object sinks, it is
enduring an increased pressure upon the whole of its external sur-
face in direct proportion to the depth, the increased upward pressure
is balanced by a proportionately increased downward pressure.
Since the law is so strictly enforced that no vessel shall proceed
to sea loaded beyond her load watermark, except under penalty,
it is of the greatest importance that the responsible authorities
should exercise the greatest care in taking the correct load
draught in the case of a vessel which has loaded aground. For
it not unfrequently happens that a vessel registers a less mean
draught immediately after becoming afloat than she did when she
was aground. After the attention already given to buoyant
pressures, the reason for this may be readily surmised. Suppose
we could take one of the cylinders shown in fig. 12, and place the
bottom surface in close contact with the bottom of the tank, so
that neither air nor water could possibly get beneath it, we
should then find that, though water surrounds it on all sides, even
to its top surface, no buoyancy pressures are experienced by the
cylinder, and therefore it has not the least floating power, even
though it is in its light condition, weighing only 12 J lbs.
But, more than this, we know that the atmospheric pressure at
the earth's surface is 15 lbs. per square inch. Hence, if neither
water nor air is capable of getting under the bottom surface of
the cylinder, not only is there no buoyant pressure, but there
is an atmospheric pressure of 15 lbs. on every square inch of the
upper outside surface of the cylinder, as well as 15 lbs. per square
inch on the internal surface of the cylinder, assuming, naturally,
that it is filled with air, and not a vacuum. There is, therefore,
a pressure of 15 lbs. per square inch on the inside bottom surface
of the cylinder. And as this bottom surface contains an area
26 KNOW YOUR OWN SHIP.
of 1 square foot, or 144 square inches, the total pressure is
144x15 = 2160 lbs., or nearly a ton, and against this there is
not the slightest upward pressure from the water.
Suppose, however, that the bottom of the cylinder is only
partially in close contact with the bottom of the tank, so that
neither water nor air could intervene over an area of, say, 10 per
90
cent, of the bottom. The buoyancy pressure would now be -— •
of 64 lbs. (supposing the water to be salt) = 57*6 lbs., while the
atmospheric pressure is 144 x -— -. x 15 = 216 lbs. The buoyancy
pressure is 57*6 lbs., and the atmospheric pressure 216 lbs. ; the
difference, 158*4 lbs., represents the preponderating downward
pressure, indicating that the cylinder will not float.
It is true, these are theoretical illustrations, though, in some
degree, somewhat similar conditions are found to exist in the case
of actual ships. It will depend upon the nature of the bottom
upon which the ship is lying, and the amount of the bottom
surface in close contact with the bottom upon which she rests.
This is the only explanation which can be given for such an
occurrence as described at the beginning of this feature of buoyancy,
Avhere a ship registers a less draught after floating than imme-
diately before when she was aground.
Reserve Buoyancy. — Let it be imagined that a vessel float-
ing at the waterline where the "tons per inch" is, say, 12 tons,
has an additional weight of 60 tons placed on board. The result
will be that the weight of the vessel having increased 60 tons in
excess of the buoyancy, she must become further immersed. But
how far 1 Well, since we have observed that 1 ton of buoyancy
equals 1 ton of displacement, she will therefore sink until she
has displaced 60 tons more water, which is an increase of — -, or
5 inches in the draught.
If, on the other hand, 60 tons be taken out of the vessel, the
buoyancy will now be 60 tons in excess of the displacement, the
result being that the vessel will rise out of the water until the
buoyancy is reduced by 60 tons, and the draught is decreased by
-— , or 5 inches.
12
Thus, we have here one of the conditions of a vessel floating
at rest in still water — namely, that the total toeight of the vessel
equals the total weight of tlie toater displaced, or the buoyancy.
The buoyancy of the immersed portion of the vessel represents
that which is requisite to keep her afloat. The buoyancy of all
BUOYANCY.
27
enclosed -watertight space above the waterline is therefore surplus
buoyancy, or safety buoyancy, or, as it is more commonly termed,
Reserve Buoyancy (see figs. 15, 16, and 18).
Sheer.— It is not sufficient that a vessel have just enough
buoyancy to keep her afloat, for if she had only this, every wave
would submerge her. It is the surplus buoyancy that gives her
rising power, and, as we shall see in Chapter VI., provides righting
power when inclined. The great advantage of sheer (fig. 18),
S^^^^v^o^^Sivca^t^caiK^^
S= Sheer. Volume above line X, Y= Reserve buoyancy obtained by sheer.
Fig. 18. — Sheeb.
which gives surplus buoyancy at the ends of a vessel, will now be
evident, for every time the vessel pitches into the trough of a
sea, she immediately displaces more water than her weight, and
is, therefore, thrown up again.
Value of Deck Erections. — The Board of Trade recognises
this to such an extent as to recommend a certain amount of sheer,
according to the type of the vessel. When this amount is ex-
ceeded, a reduction in the freeboard is allowed, and when the
sheer is less an addition is made to the freeboard (see chapter
on " Freeboard "). The value of poops and forecastles, especially
the latter, and particularly if efficiently closed at the ends, will
now be clearly understood, since they all add to the buoyancy,
and at those parts of the vessel where it is greatly needed.
Though not to the same extent in efficiency, yet all bridges
with watertight ends, and deck houses and hatches — in short, all
enclosed watertight erections afford reserve buoyancy.
Centre of Buoyancy. — Now, just as the Centre of Gravity
of the weights ranged on a lever can be ascertained, as explained
in the previous chapter, so the centre of action of the numerous
forces of buoyancy may be found; and since the forces acting
upon any body may always be supposed to act directly through
the centre of action, the value of this point will be readily
granted, especially when we come to deal more closely with
the subject of Stability.
However, instead of speaking of the centre of action of the
forces of buoyancy, this point is, for brevity, termed the Centre
of Buoyanaj* and, moreover, it is found that the centre of
buoyancy is the centre of displacement. Thus, to find the centre
♦ B in figa. 16 and 16.
28
KNOW TOUR OWN SHIP*
of buoyancy it is simply necessary to calculate the centre of dis-
placement, as the two names indicate exactly the same poinjb.
The centre of buoyancy being the centre of the displacement, it
must vary in position with every variation of draught, so that it
becomes necessary to arrange a convenient method of readily
ascertaining the centre of buoyancy at any draught. This is done
by calculating the centres of buoyancy at several draughts
parallel to the load waterline, and constructing curves. By means
of a calculation of moments, using horizontal areas of waterplanes,
instead of weights as in the case of the lever examples in the
previous chapter, the positions of the vertical centres of buoyancy
are found at the required draughts. In a similar manner the
longitudinal centres of buoyancy at several draughts are calcu-
lated, and by using vertical areas of transverse sections of dis-
placement at regular intervals fore and aft instead of weights, the
several longitudinal centres of buoyancy may be found. See
Chapter X. for examples of calculations.
C.B.= Centre of buoyancy.
Fig. 19.— Centre of Buoyancy of Box-shaped Vessel.
Curves of Vertical and Longitudinal Centres of Buoy-
ancy. — Thus, to find the actual centre of buoyancy, it is
necessary to construct two curves, one for the vertical centres of
huoijancy, to give vertical position, and the other for the
longitudinal centres of buoyancy, giving longitudinal position.
The intersection of the two lines is the point required.
These curves, at the expense of little time and trouble, can be
Supplied to the ship's officer by the shipbuilder or naval architect.
To construct curves for a box-shaped vessel would be un-
necessary, as it is evident that the vertical centres of buoyancy
must always be at half the draught (see fig. 19), and the
longitudinal centres of buoyancy at the middle of the length if
floating with the bottom parallel to the waterline.
Thus, at 10 feet draught, the vertical centre of buoyancy
is 5 feet down from the waterline, at 6 feet draught it is 3 feet
down from the waterline, and so on.
Si,HOiaH dO 3-|«9e
30 KNOW TOUR OWN SHIP.
Curve of Vertical Centres of Buoyancy. — The heights
of the vertical centres of buoyancy used in the construction
of the curve in fig. 20 are for a vessel about 200 feet long, and
with a draught of 14 feet when fully loaded. Suppose the
vertical centres of buoyancy at the 4, 8, 12, and 16 feet draughts
are found to be 1-2, 2-9, 4*9, and 6*6 feet respectively below
their respective waterlines. To construct the curve proceed as
follows : — Draw the lines A B and A C at right angles to each
other. Let A B represent a scale of heights and A C a scale of
draughts. Through the 16 feet height in the scale A B draw a
horizontal line as shown, and through the 16 feet draught in A C
draw a vertical line intersecting the other at D. From the point
D set down the distance of the centre of buoyancy below the 16
feet waterline = 6'6 feet. Proceed in the same manner for the 12
feet waterline. Through the 12 feet height draw a horizontal
line, and through the 12 feet draught draw a vertical line inter-
secting the other at E. From E set down the distance of the
centre of buoyancy below the 12 feet waterline = 4*9 feet. In a
similar manner the centres of . buoyancy at the 8 and 4 feet
waterlines may be set off. Through these points draw the line
X y, which is the curve of the vertical centres of buoyancy required.
By means of it the height of the vertical centres of buoyancy
above the bottom of the keel may be read off at any draught.
It will be understood that the curve constructed for any
particular vessel will be of little use for any other vessel unless
of exactly the same form and proportion in the immersed portion
of the hull. But for the sake of example, let the curve in
fig. 20 be for a yacht with a rising keel and drawing 10 feet
forward and 13 feet aft. This represents a mean draught of
=11 feet 6 inches. At 11 feet 6 inches on the horizontal
2
scale of draughts, set up a vertical line until it intersects the
curve of the centres of buoyancy. From this point draw a
horizontal line until it meets the vertical scale of heights, and
there we read 7 feet, which is the height of the vertical centre
of buoyancy above the bottom of the keel. Had the vessel been
an ordinary cargo one, floating on even keel, and drawing 11 feet
6 inches fore and aft, the height of the centre of buoyancy would
have been the same. As has already been stated, this point,
taken by itself alone, is of little use to anyone. It is only when
used in relation to other points, with which we shall deal, that it
possesses importance.
Curve of Longitudinal Centres of Buoyancy. — The
longitudinal centres of buoyancy for the same vessel of which fig.
20 is the curve of the vertical centres of buoyancy are found to bo
BUOTANCT. SI
98'7, 99'2, 99-8, and 100 feet from the afterside of the stem post
at the 16, 12, 8, and 4 feet waterlinea respectively.
The curve would be constructed in the following manner (fig.
21):-
Draw the vertical line A B, and upon it construct a scale of
draughts. From E draw the homontal line B C, and upon it
construct a scale of feet, long enough to include the greatest
distance of the centre of buoyancy from the stem post, which in
this case is 100 feet. 98-7 feet on the line B C gives the first
point in the curve. At 12 teet dranght draw a horizontal line,
and through the point iu the scale indicating 99"2 feet drop a
vertical line. The point of intersection gives the second point in
SCALE ■or FEET
■*
]^
^
p
in
R
S
+
2.
/
FiQ, 21.— Curve of Lokojtcdisaii Cestees of Buoyakcy.
the curve. Proceed in the same manner with the 8 and 4 feet
waterlines, obtaining the points indicated by the large dots.
Through these points draw the line x y, which is the eune of the
longitudinal ce:itres of buoyancy. Supposing we are asked to read
off the longitudinal centre of buoyancy at, say, 7 feet 6 inches
draught, we draw the horizontal line from the 7 feet 6 inches
height in the scale of draughts until it intersects the curve, and
from this point we strike a vertical line to the scale of distances,
and there is indicated 99'6 feet from the afterside of the stern
post. From this curve we can see that since the vessel is 200
feet long, the displacements of the fore and after bodies are
32
KNOW YOUR OWN SHIP.
exactly equal at the 4 feet draught, as the vessel's centre of
support (centre of buoyancy) is at the middle of the length.
Then, as the draughts increase, we notice that the centre of
buoyancy travels a little towards the stern, showing that the after
body is slightly fuller than the fdre body, increasing in this respect
up to the load waterline. Now, we have simply reduced our ship
to a huge lever, balanced practically- at the centre when floating
at 7 feet draught. Suppose in this condition the vessel weighs
550 tons, this being her displacement. She is then to be addition*
ally loaded in the following manner : —
r»0 tons are placed 20 feet abaft of the longitudinal centre of buoyancy.
30 ., .. 60
20
40
ft
ti
if
30 feet forward
70
f)
It
it
if
it
a
if
if
a
fi
What effect will this have] First of all, we know that the
draught will be increased. This could be found before the weights
are placed on board, by adding the weights together, and referring
to the displacement scale in figs. 3 and 4.
550 + 50 + 30 + 20 + 40 = 690 tons, which reads 8 feet 4 J inches
mean draught.
There may be another effect. If the moments of the weights
preponderate ahead or astern of the centre of buoyancy, then the
vessel will trim* by the head or the stern, as the case may be.
Let us see —
Moments on after side of Centre
of Buoyancy.
50 X 20 = 1000 foot-tons.
30 X 60 = 1800 ,,
Total, 2800
fi
Moments on fore side of Centre
of Buoyancy.
20 X 30 = 600 foot-tons.
40 X 70 = 2800 „
Total, 3400
II
Then, since the moments preponderate on the fore side by
3400 - 2800 = 600 foot tons, the vessel will trim by the stem.
But suppose we now wish to know what weight must be placed
at, say, 25 feet aft of the centre of buoyancy to bring the vessel
again on even keel — that is, with the new load line parallel to
the keel. This would be discovered by dividing the foot-tons in
excess by the distance the new weight has to be placed from the
original centre of buoyancy. The result will be the required
weight —
600
25
= 24 tons.
* By ti'im is meant the difference between the draught at the stem, and
the draught at the stern.
BUOYANCY. 33
' It will now be seen that the moments on each side of the centre
of buoyancy are equal.
Vessels passing from salt or sea water to fresh or river water
increase in draught. The reason of this has already been
explained.
Effect of Wedges of Buoyancy on Ship's Centre of
Buoyancy. — Another thing which may be observed is, that not
only do some vessels change draught in passing from sea to river
water, but that they also change trim. The reason of this will be
evident when it is known that in some vessels the fore body is
fuller, and has more displacement than the after body. There-
fore, in increasing in draught, the longitudinal centre of buoyancy
•will travel forward (since it must remain in the centre of displace-
ment), and the fore end of the vessel, having more support, will
sink less than the after end. Hence, the change of trim.
In lecturing before ships' officers, the question has more than
once been asked : Is it possible, with a vessel trimming by the
stem and the centre of the disc on the load waterline, to place
any more cargo on board and yet not submerge the disc, and, con-
sequently, not increase the draught ?
To such a question it is certainly possible to answer " yes," but
such a vessel would be so exceptional in her design that the answer
is practically " no."
For on examination of the lines of ordinary vessels, it is
generally found that the fore body is slightly fuller than the
after body, but this fulness takes place usually on the lower lines.
At the region of the load line, however, the greatest fulness is
usually aft, so that, imagining the vessel to be floating first at
the waterhne W L (fig. 22), and then by shifting weights forward
i'lG, 22. — Wedges of Buoyancy.
to float at A B, the wedge y would generally be of greater volume
than X.
We have already seen that before a vessel will float at rest at
any waterline, the weight of displacement and the buoyancy must
equal each other. If by any means the weight of displacement
be increased, the vessel will increase in draught ; if by any means
the buoyancy be increased, the vessel will rise out of the water,
and the draught will be decreased.
34 KNOW YOUB OWN SHIP.
Thus it follows that if the fore wedge x be less in volume than'
the aft wedge y, the draught would actually be slightly increased
since the buoyancy is less. If x and y be equal, no change will
take place in the draught, and only when x is greater than y would
any reduction in the mean draught be observed. Such is not
likely to occur except in ill-designed vessels, for the effect upon
the speed by the production of great resistance would certainly
outweigh the consideration of carrying a trifle more deadweight at
such a cost.
Again, suppose the vessel to be floating at the waterline A B,
and weights to be then shifted aft, so that the waterline is now
at W L. If the volume of the immersed wedge y is more than
the emerged wedge x, the draught will be somewhat decreased,
and if y be less than Xj an increase in draught would occur. We
have observed that the vertical centre of buoyancy is the vertical
centre of the displacement, and that with every transverse move-
ment of the vessel (whether by means of external force in river or
dock, or under the influence of wind or waves) there is. a corre-
sponding movement of the centre of buoyancy into the new centre
of displacement. We shall now see how this new position may be
found, and in this again the study of moments (Chapter II.) comes
to our assistance.
Fig. 23 is a cylinder 10 feet in diameter, 20 feet long, and
floating at 5 feet draught. The displacement in this condition
would be J X 10^ x -7854 x 20 = 785*4 cubic feet. B is the centre
of buoyancy when floating upright. Let the cylinder be inclined
to an angle of 20°. Observe clearly what takes place. W L was
the original waterline ; after the inclination the waterline is W' L',
so that the wedge A, which was previously actual buoyancy, has
come out of the water and become reserve buoyancy, and the
wedge B, which was formerly reserve buoyancy, has become actual
buoyancy. (Let g and k be the centres of buoyancy of each of
the wedges.) This simply amounts to shifting the wedge of
buoyancy, with g as its centre, to the position of the wedge, with
k as its centre, a distance of about 6J feet. Let the wedge, with
g as its centre, equal 87 cubic feet, and, as just stated, the distance
from the centre of buoyancy of the emerged wedge to the centre
of buoyancy of the immersed equal 6J feet As the volume of
displacement must be the same, at whatever angle of inclination,
it follows that the wedge, with k as its centre, will equal 87 cubic
feet. Now the new centre of buoyancy of the whole figure must
have travelled in the direction in which the actual buoyancy was
shifted ; that is, to starboard of its original position in the figure
— viz., to B^, and in a line parallel to the line joining g and k, the
centres of the wedges. The exact distance may be found by
BUOYANCY.
3&
multiplying the volume of the wedge of buoyancy moved, 87 cubic
feety by the distance moved, 6^ feet, and dividing by the total
volume of displacement ; or, in other words, the volum^e of buoy-
ancy.
^ ^ = 'J2 feet, centre of buoyancy moved to starboard.
In coming to vessels of ship form, the principle of finding the
shift of the centre of buoyancy is exactly the same, but there is
I*
(cylinder floating upright
Star
69)
Cylinder inclined to 20%
Wedges of immersion and emersion.
FiQ. 23.— Wedges of Buoyancy in a Cylinder.
a difference in the wedges. In one respect, however, the two
wedges in any one ship do not differ, and that is, that the volume
of the wedge of immersion is always equal to the volume of the
wedge of emersion. In cylindrically-shaped vessels, whose water-
line passes through the centre of the cylinder, revolving as they
do on the centre of their diameter, not only are the wedges equal
in volume, but identical in shape, any sections of the wedges all
fore and aft being exactly similar. This is not so with vessels of
ship form, for in these the wedges of immersion and emersion vary
36 KNOW YOUB OWN SHIP.
very considerably in form, especially towards the ends, and even
more so still if the angle to which the vessel is inclined be
great.
A little thought or personal observation of the actual form of
a ship's hull will make this the more clear.
Thus, while it is a simple matter to find the centre of gravity
of the wedges of immersion and emersion of a floating cylinder —
whose waterline passes through the centre of the cylinder — it
entails more work to find the corresponding points in an actual
ship ; and, while involving a considerable amount of labour, is not
a matter of serious difficulty. (See Chapter X. for samples of
Calculations.) *
Effect of Entry of Water upon Buoyancy. — There is still
another aspect of the subject of Buoyancy which calls for some
attention. Suppose, first of all, that by some means or other a
quantity of water enter the hold of a vessel. What will be the
effect ? This will all depend upon how the water entered. Let
us imagine that the sea breaking over the bulwarks entered by
means of some deck opening — hatchway, for instance — the outside
shell plating of the vessel being intact and perfectly watertight.
The result of water finding ingress in this way would exactly
resemble the result of loading cargo, the water being deadweight
at the rate of 35 cubic feet to 1 ton. Should water continue to
enter the vessel, the draught w^ould gradually increase until, if it
happened that the total weight of the vessel, cargo, and water in
her were more than the maximum possible displacement, she would
naturally sink. If, on the other hand, when the hold was filled,
the total weight of the vessel and the water in her were less than
the maximum possible displacement, she would remain afloat —
that is, disregarding the effect such might have upon the stability
of the vessel, and also taking it for granted that little change of
trim took place ; for otherwise, should the water find ingress into
a large hold towards the end of a vessel, this might result in her
going down by the head or stern, as the case might be. But let
us take an entirely diff'erent case. Supposing the outside plating
in the way of some hold be damaged below the load waterline, the
sea would consequently russh in. If the hold were empty, it would
fill, unless prevented, up to the level of the outside sea level, with
water. But this is diff'erent from the former case, where water
was poured into the hold from above. There the water acted as
deadweight, but not so in this example, as there is now free com-
munication between the water in the hold and the sea outside.
What has happened is this : The vessel has been robbed of the
total buoyancy, both actual and reserve, of this compartment, evea
though it be found that, after increasing in draught, she still
BUOYANCY.
37
floats with considerable freeboard. The empty space from the
water in the hold to the top of the hatchway, as stated, is no
longer reserve buoyancy, and the vessel has lost the entire
buoyancy of this compartment ; and if it happens that the total
buoyancy of the other intact compartments of the vessel is greater
than the total displacement, as it was before the structure was
damaged, and before the water entered, the vessel will float. If,
ou the contrary, the vessel possesses less remaining buoyancy
than this, she will be entirely immersed, and will sink. This will
perhaps be somewhat clearer if illustrated by a box vessel, as
shown in &g, 24. The vessel is divided into three watertight
1
w
A
i-^— -"^-s.^
A
L
"■'
B
IIS^
B
Fig. 24. — Effect on Bfoyancy of Entry of Watek into
A Damaged Compaetment.
compartments by two watertight bulkheads, and floats at the
waterline, WL. The centre compartment is damaged, and its
actual and reserve buoyancy entirely lost, the sea having free
entrance. If the sum of the volumes of A A (the reserve
buoyancy) and B B (parts of the original actual buoyancy) be at
least equal to the original actual buoyancy — that is, to the whole
of the volume below the original waterline — it is possible for the
vessel to float ; if it be less, she will inevitably sink.
The reader must bear in mind that the inflow of water into
such a hold as this has added nothing whatever to the weight
of the ship, althougli the draught has increased ; the weight, or
the total displacement, remains exactly the same, but the entire
empty space in the damaged hold is to be left out altogether, and
ignored in reckoning upon the actual and reserve buoyancy. In
increasing her draught, the vessel has simply taken from the
reserve buoyancy in the other watertight and intact compart-
ments a volume equal to the volume of that part of the damaged
compartment which was previously below the waterline, and
which was, therefore, previous to the accident, in use as actual
buoyancy.
Again, suppose this accident happened to the vessel when her
hold was filled with cargo, say timber, for example. How does
she stand now ? The water will flow into the hold, and occupy
vfh&t space it can. This will naturally be very small indeed, since
38 KNOW TOUR OWN SHIP.
the hold is already practically full. As the water cannot possibly
occupy the space taken up by the timber, it has to be content
with what remains. Therefore, the volume below the original
waterline of all the corners and crevices not occupied by the
timber is lost actual buoyancy, and the vessel will sink until she
has taken from the reserve buoyancy a volume equal to the
volume of the space unoccupied by the timber, and below the
original waterline, which, in most cases, would be comparatively
little.
Camber or Round of Beam. — Vessels classed at Lloyd's
require that all weather or uppermost decks have a round upon
them, or camber, of at least j inch to 1 foot of beam. Thus, a
vessel of 40 feet beam will have a camber of J inch x 40 = 10
inches, and will, therefore, be 10 inches deeper at the middle of
the breadth at midships than at the sides. One important
advantage to be gained by this is an addition to the reserve
buoyancy, and, little as it may seem, its importance is so re-
cognised, that, if the stipulated amount of camber be reduced, an
increase of freeboard is demanded ; if the amount be exceeded, a
reduction in the freeboard is allowed. (See chapter on "Free-
board.")
Testing Water Ballast Tanks. — All water ballast tanks
should be tested, in order to ensure that all joints and connections
of plates and angle bars and the caulking be thoroughly watertight.
This is done by means of water pressure. An iron pipe of the
required length is fitted vertically into the top of the tank which
is about to be tested. Water is then pumped into the tank until
it is forced out at the top of the pipe. To accomplish this,
considerable pressure has to be applied, which is in direct
proportion to the height of the pipe.
Supposing the pipe to be 1 square inch in sectional area and 20
feet long from the crown of the tank, at the moment the tank is
just full there is no pressure whatever upon the crown, but as
soon as the water overflows at the top of the pipe it is evident
that there must be a pressure at the bottom of the pipe of
20 X 62i
't — ^ =8*6 lbs. (fresh water). The pressure upon the inside
of the crown of the tank must also be 8*6 lbs. per square inch or
20 X 62|= 1250 lbs. per square foot.
Lloyd's requirements for the testing of tanks in vessels classed
by them is as follows : —
Double Bottoms. — To have a head of water at least equal to
the extreme draught — that is, the pipe previously mentioned must
extend to the height of the maximum load line.
BUOTAXCY. 39
Deep Tanks and Peak Tanks, — To have a head of water at least
6 feet above the crown of the tank.
Fore and After Peak Bulkheads without Peak Ballast Tanks, —
These are required to be tested by filling the peaks with water to
the height of the load line. Other Bulkheads and Decks may have
their watertightness tested by playing a hose upon them with a
good head of water.
40 KNOW TOUR OWN SHIP,
CHAPTER IV.
STRAIN.
Contents. — Relation of Weight of Material in Structure to Strength —
Strain when Floating Light in Dock — Relation between Weight and
Buoyancy — Strain Increased or Decreased in Loading— Distribution
and Arrangement of Material in Structure so as to get Greatest
Resistance to Bending — Types of Vessels Subject to Greatest Strain —
Strains among Waves — Panting Strains — Strains due to Propulsion by
Steam and Wind — Strains from Deck Cargoes and Permanent Weights —
Strains from Shipping Seas — Strains from Loading Cargoes Aground.
Relation of Weight of Material in Structure to Strength. —
It would be rather absurd to commence the study of the struc-
ture of ships — whether they be steamers, sailing ships, or yachts —
before first having some knowledpje of the strains which, under
varying circumstances, they would most probably have to bear.
To build a ship capable of enduring, without damage to its
structure, every possible strain which might be brought to bear
upon it, however excessive, would necessitate the introduction of
such an amount of heavy material into its structure as to render
it greatly deficient in its carrying capacity. It does not even
follow that the vessel with the heaviest material is necessarily
the best, or even the strongest, ship, but rather the one with the
lightest material so combined as to give the maximum strength
and efficiency, and sufficient to cover the strains which in all
likelihood, under reasonable circumstances, would have to be
endured. This is the aim of all such classification societies as
Lloyd's, Bureau Veritas, The British Corporation, etc.
Ships are built on a combination of two systems of framing
— viz., longitudinal and transverse.
Longitudinal framing includes all those parts in the frame-
work of a vessel which run in a fore and aft direction, whose
function is to afford longitudinal strength.
Transverse framing includes all those parts in the frame-
work of a vessel ^hose function is to give transverse or athwart-
ship strength. ^
As has been aftteady indicated, the strongest ship is only
obtained when thesa two systems have been intelligently woven
together, the strengt* of the one co-operating with the strength
of the other — that is\ in relation to the work which they have
STRAIN.
41
to do. When this is accomplished the whole is then covered by
a skin in the form of a shell-plating and decks, and by this
means the skeleton or framework of the ship is still further
united and strengthened.
Strain when Floating Light. — Looking at an ordinary cargo
steamer floating in the dock in her light condition, and lying at
rest at her moorings, one would almost imagine at first sight
that she is perfectly free from strain. But on investigation
this is found not to be so. As ha^ been previously shown, any
object placed in w^ater, whether it be a ship or a log of wood,
will sink until it has displaced a volume of water equal in
weight to itself. Or, in other words, before the object will
remain stationary, and at rest at any waterline, the downward
Figs. 25 and 26. — Stkains on Vessel Floating Light.
pressure of the weight of the object floating must be exactly
balanced by an equal upward pressure of the water.
Relation between Weight and Buoyancy. — Supposing the
vessel shown in fig. 25 be 200 feet long, and classed at Lloyd's,
ehe would require four watertight bulkheads, one at each end of
the engine and boiler space, a collision bulkhead at the fore end,
and another bulkhead at the aft end. The weight of the vessel
light being, say, 500 tons, if placed in the water would displace
a volume of water 500 tons in weight, and would thus remain
stationary, say, at the waterline, W L.
But suppose the vessel could be divided off into five separate
parts at the four watertight bulkheads, and each part floated
separately, as shown in the sketch (fig. 26). It will now
be seen that the draughts vary for each part, and none of them
float at the original waterline. A little observation will soon
explain this. The total weight of all the parts is exactly the
same, and therefore the total water displaced is the same ; but
42 KNOW YOUR OWN SHIP. '
throughout the length of the vessel there is an unequal distribu-
tion of weight and buoyancy. Thus, for example, referring to
the sketch, parts 1 and 5 — the euds of the vessel — ^being very
fine, and yet of considerable weight, which is increased by the
poop and forecastle, in order that they may be balanced by the
buoyancy they will have to sink to the draught as shown. In
parts 2 and i we have the vessel rapidly increasing in internal
capacity or fulness, and small in weight in comparison with the
volume of the enclosed space, the result being that these parts
float at a less draught than previously. In No. 3 we have the
fullest part of the vessel with greatest floating power. But in
this compartment is concentrated the weight of engines and
boilers, which tends to increase the draught upon what it is in
the combined ship. Thus we see that throughout the length
there is a series of upward and downward vertical strains, as
shown by the arrows, tending to alter the form of the vessel
longitudinally. Note that these strains tend to alter the form of
the vessel. This alibrds one consideration for the naval architect
or shipbuilder, in constructing an efficient ship — viz., that
there is sufficient strength to prevent any such alteration in
form taking place, or even any sign of such sjbrain being endured.
Strains in Loading, — Now it can easily be seen how these
strains may be considerably increased when loading ; for
instance, if in the case of a miscellaneous cargo the heavy
weights be placed towards the ends of the vessel where the
buoyancy is least, the tendency of the ends of the vessel to
droop would be greatly aggravated. The endeavour should be
to distribute the heavy weights of the cargo so as to produce a
balancing effect between the forces of weight and buoyancy, and
thus avoid great local excess. By this means it is possible to
reduce the strain even from what it is in the light condition.
In considering strains at sea, the evil of bad loading will be
seen still more clearly.
In addition to these vertical strains to which the vessel is
subject while lying at rest, there are collapsing strains acting
upon every portion of the immersed skin of the ship (see
fig. 15, Chapter III.). For, be it remembered that the forces
of buoyancy act in perpendicular lines to the immersed surfaca
Thus, while there is an upward pressure tending to thrust the
vessel out of the water, there are also horizontal and oblique
forces tending to crush in the sides of the ship.
It will be obvious that the greater the immersed girth of the
vessel, the greater the strain. Thus, the strain is greatest at
midships, and on each side of midships ; and towards the ends, as
the vessel becomes finer, it gradually diminishes. Considerable
STRAIN.
43
as strains in still water may be under certain circumstances,
on investigating the strains experienced at sea we shall see how
enormously they are increased.
First, observe the strains endured by a ship in the condition
shown in fig. 27. Here the vessel is supported at midships
on the summit of a wave, the extremities being practically
unsupported. The ships may now be compared to a hollow
girder with weights ranged miscellaneously throughout its length,
Figs. 27 and 28. — Stbains of Vessels on Waves and in Thougks.
and supported only at the centre, the result being a severe
hogging strain tending to make the ends droop.
Distribution of Material to Resist Bending. — The question
now arises, How should the material employed in the con-
struction of the vessel be distributed so as to withstand this
tendency to bend?
In fig. 29, let A 6 be a bar of iron or steel 100 feet long,
supported at the middle of its length, and with a weight of
10 tons attached to each end. This would not be an exact
illustration of a loaded vessel supported at midships upon a
wave as in fig. 27, but it will form a fair approximation to the
strains experienced by a vessel when in a light condition with
large peak ballast tanks full, or it will show the evil of loading
a vessel with the heaviest cargo at the ends, and will serve to
illustrate the principle it is wished to make clear. Let the
sectional area of the bar be the same throughout its length.
The bending moment of each weight would be 10 x 50 = 500
foot-tons, and the tendency of the bar would be to bend or
break at the point of support since the strain is greatest at this
point. The tendency to break at 10 feet on each side of the
support would be 10x40 = 400 foot-tons, and at 20 feet from
44
KNOW YOUR OWN SHIP.
the support 10x30 = 300 foot-tons, and so on, the tendency
to break diminishing towards the ends as the leverage decreases.
^^a
4<- — So* —
B
@
Fig. 29.— Strain on a Bab Loaded at each End.
The bending moment at any section from the centre to the end of
the bar might be graphically illustrated in the following manner : —
---^ ^-— I. ^
Fig. 30. — Distribution of Bending Moment.
Let "W «=» weight hung at each end of bar.
,, L = hair-length of bar (that is, length from centre to end of bar).
,, M = maximum bending moment (which occurs at centre of bar).
Make M equal weight multiplied by leverage — W x L -» 10 x 50 — 600
foot- tons at the middle of the bar.
Join W.
Let M be set off to any arbitrary scale ; then by using the
same scale the bending moment can be measured at any inter-
mediate position between the support and the weight. In a
similar manner the strains experienced by a vessel supported at
the middle of her length upon a wave are greatest in the region
of the half length amidships. The structural arrangements in-
troduced, and the great value of such erections as long bridges
over the middle of the length in alibrding strength to resist those
bending strains, will be shown at a later stage.
Now, supposing the bar in figs. 29 and 30 to be 4 square
inches in sectional area, the question may be asked. Is it possible
to arrange the material, preserving the same sectional area so as
to get greater efl&ciency in resisting longitudinal bending % Let
the bar be rolled out so as to make it 8 inches by \ inch in
section (same sectional area as previously), the length remaining
STRAIN. 45
the same. It will easily be seen that if the bar (or plate, as it
now is) be supported as before with the wide 8-inch side hori-
zontal, and the weights attached to its extremities, that it
possesses less resistance to bending than when the bar was square
in section.
But should the bar be supported with its wide 8-inch surface
vertical, it will be found that its resistance to bending has been
increased beyond what it was in the square section of the bar.
Let us make a brief examination of this difference of resistance to
bending with the same sectional area.
Let fig. 31 represent the 8-inch by |-inch plate, placed with
3
Fio. SI.—Bbnding Resistance of Bar placed Vertically.
the 8-inch side vertically, and let A B be the neutral axis. (The
neutral axis is an imaginary line of no strain passing longitudinally
through, say, the centre of depth of the plate. Since the plate is
8 inches deep, it will be 4 inches from each edge.) Supposing a
weight be attached to each end of the plate, observe what must
take place before it can bend. On the upper edge there must be
considerable expansion or elongation, and on the lower, contraction
or compression. The wider the plate is made, the greater will be
the resistance to tensile strain on the upper edge, and compressive
strain on the lower. It will also be found that the nearer the
neutral axis is approached, the less elongation and compression
are required to result in the same amount of bending, and at the
neutral axis there is neither elongation nor compression.
Now, theory and experiment agree in showing that the stretch-
ing and compressive stresses at the top and bottom edges are now
(8 inches by J inch, wide side vertical) only one-fourth of what
they were when the bar was square in shape (2 inches by 2
inches), and only one-sixteenth of what they are when the bar is
8 inches by J inch, but laid with its thin edge vertical (the for-
mally stated law is that the resistance of the bar to this kind of
stress varies directly with tlie square of the dejpth of tlie bar,
and directly as its breadth).
The resistance to bending, moreover, will be greatly increased
if the vertical plate be turned into a girder by attaching a bulb
46
KNOW TOUR OWN SHIP.
to its upper and lower edge, as shown by A in fig. 32, or by
adding strengthening flanges to the upper and lower edges, where
the tensile and compressive strains are greatest ; for example, see
IITTX
ABC D E F
Fio. 32. — Bending Resistance of Girders.
fig. 32, B, C, D, E, and F. (Stress, Strain, and Strength are dealt
with much more exhaustively in the author's companion volume to
Know your own Ship,)
Tjrpes of Vessels subject to Greatest Strain. — The prin-
ciples which apply to a plate or girder apply equally well to a ship,
for, after all, a ship is simply a huge, hollow girder, and from the
foregoing reasoning the following deductions may be made :—
1st. That vessels of great length, and therefore subject to
excessive bending moment among waves, require more longi-
tudinal strength than short ones (not necessarily more trans-
verse strength). •
2nd. That long, shallow vessels possessing less resistance to
tensile and compressive strains require additional longitudinal
strength.
3rd. That in all vessels more strength is required in the
region of midships, while a reduction may be gradually effected
towards the ends.
Strains among Waves. — In studying the case of a ship in
the condition shown by fig. 28, it is observed that since the
ends are supported on waves, and the midship part, containing
engines, boilers, bunkers, etc., is to a large extent unsupported,
the vessel, especially if a long one, will endure a severe sagging
strain tending to make her droop amidships. There are cases
on record where long, shallow vessels have actually fractured
through the middle and sunk. The vessel may now be com-
pared in some measure to a bar, supported at the ends with a
weight in the centre, thus —
—jp:
SOL^^A
Fig. 33.— Bak Weighted ik the Centre.
STRAIN.
47
and if the weight be, say, 10 tons, and its distance from each
support 50 feet^ then by the following diagram the bending
moment may be illustrated : —
Fio. 34. — Distribution of Bending Moment in Bab.
Here, 10 tons in the middle gives 5 tons pressing on each
support, and the bending moment in the middle ( =» pressure x
leverage) = 5 tons x 50 feet = 250 foot-tons = M.
Set off M (250) to any scale, and join CB and CA. By
using the same scale, the bending moments can be measured at
any intermediate position between the support and the weight.
Here again in this illustration it is shown that the longitudinal
bending moment is greatest at the middle of the bar correspond-
ing to the midship portion of the ship, decreasing towards the
ends, where it vanishes altogether. This provides another reason
why vessels should have greater longitudinal strength amidships
than elsewhere.
Moreover, owing to the rapid transit of the waves, and, there-
fore, the unequal distribution of weight and buoyancy, the
Fig. 35.— Strains due to Rolling among Waves.
vessel is subject to a succession of severe and sudden strains.
It will also be seen that in rolling among waves, there is a great
tendency for a vessel to alter in transverse form. Under such
circumstances, she may be compared to a box, as shown in fig. 35.
48 KNOW TOTTR OWN SHIP.
If a series of irregular, collapsing strains be put upon the exterior
of the box, the tendency is not so much to fracture in the positions
shown by the wavy lines, but to work at the corners. Exactly
the same thing takes place with a ship at sea as she rolls among
the waves. The strain tends to have the effect shown in B, fig.
35.
Thus in determining the size and arrangement of all material in
the construction of ships, there must be sufl&cient longitudinal
strength to resist all longitudinal, bending forces, and sufficient
transverse strength to resist all collapsing forces or alteration to
transverse form of the nature already described, with a reasonable
margin for safety.
As has been already shown, it is not necessary to have as much
sectional area of material towards the ends of the vessel as near
amidships, since the strain is less ; but, nevertheless, in com-
parison with the strain which has to be borne, both sections
should be equally able to withstand such strains as come upon
them, for it should be remembered that the vessel is no stronger
than her weakest part.
Thus far, only strains affecting the ship as a whole have been
considered, but there are several other strains it is necessary to
take into account which only affect the vessel locally.
1. Panting Strains, — The fore end of the vessel, especially when
of a bluff form of stem and driven at a high speed, being the first
part to pass through the water, naturally suffers great head
resistance, tending to make this part pant or work in and out.
2. Strains due to Propulsion by Steam, — These strains may be
divided into (1) strains owing to weight of engines and boilers,
and (2) strains due to vibration of shaft, etc.
3. Strains dice to Propulsion by Sail, — In vessels with lofty
masts and much sail area, great strain is transmitted^ to the hull
through the masts by the force of the wind and the action of
rolling.
4. Strains owing to lieavy j^^rmanent weights carried, such as
winches, windlass, cranes, anchors, guns, etc.
5. Strains from Deck Cargoes, — It is customary with many
vessels, such as those engaged in the " Baltic " trades, to carry
coal or some other British export on the outward voyage, and to
return with cargoes of timber, and in order to get the vessel down
to her load waterline large deck cargoes are carried. Many of the
shipmasters engaged in such trades are not unacquainted with the
fact that, owing to the heavy deck weight, these vessels ai'e
severely strained, and sometimes take a set or sort of twist, and
this is only discovered after the cargo has been removed, and
perhaps not until even a few days later still, when the vessel,
STRAIN. 49
sometimes with a considerable report, frees herself from her
strained condition with a severe trembling from stem to stern.
On examination it is found that very many of the rivets in the
heads of the hold stanchions or pillars have been sheared, and
considerable damage done to the beam knees. This is an
abundant proof that vessels intended to carry heavy deck cargoes
require special strengthening.
Such damage as that just explained might often be obviated by
wedging or shoring the space between the top of the hold cargo
and the beams, thus assisting the beams in enduring the strain
of the deck cargo.
* 6. Strains from the shipping of seas against poop or bridge
fronts. Bridge and poop fronts with closed ends are subject to
sudden and severe strains owing to the shipping of heavy seas,
which will evidently spend their force against these bulkheads.
Such parts, therefore, require special attention, and it is only
possible to secure the maximum allowance on the freeboard when
these parts are most efficiently constructed.
7. Strains from Loading Cargoes Aground, — Vessels engaged
in trades where it is known that they will lie aground during the
operation of loading and unloading, require special stiffening on
the bottom. And so on, cases might be enumerated where,
special strain having to be endured, special strengthening must
be provided.
Excessive strains, such as those borne by a vessel when run
ashore, as frequently happens, so that one end only is water-borne,
or where the vessel, possibly laden with a heavy cargo, is laid
across a sandbank, with ends unsupported when the tide has left
* Strains from the shipping of heavy seas on deck are often more severe
than is generally supposed, as shown by the following illustration. A fine
new steel steamer, of nearly 4000 tons gross tonnage, was crossing the Atlantic
in bad weather, in the beginning of the year 1899, when she shipped a heavy
sea over the port side just in front of the bridge. The water fell with terrific
force upon the fore main hatch and the deck. The hatch coamings on the
port side were burst away, and the sea poured down into the fore main hold,
damaging a considerable amount of cargo. Beams and stanchions were sprung
and bent, the rivets in the beam knees sheared, and the deck considerably
damaged. The sea, in sweeping over the starboard side, carried nearly the
whole of the bulwarks with it. All this damage was caused by the shipping
of a single sea, for the vessel shipped very little water afterwards, which gave
the crew an opportunity of temporarily closing up the damaged hatchway.
The vessel was comparatively new, being built to Lloyd's highest class in 1898,
yet it seems quite certain that if she had shipped another sea of a like nature,
she would have foundered, and contributed to swell the list of vessels
"unheard of" or "missing." Too much attention cannot be paid to the
thorough protection of all deck openings, both hatchways and engine casings,
for it is very probable that the loss of most of those vessels which are never
again heard of is caused by accidents of a similar nature to that just described.
50 KNOW YOUR OWN SHIP.
her, the shipbuilder cannot attempt to cover, but all strains, such
as those already mentioned, may be thoroughly provided against.
A vessel in dry dock, unless carefully shored, may be consider-
ably damaged. Cases of dry docking, where the bilges have
drooped, have occurred through carelessness or ignorance. Having
briefly enumerated the chief strains borne by a vessel under
various circumstances, the reader will now be better prepared to
understand why exceptional strength is introduced into the
structure, either considered as a whole, or in particular parts only.
STBUCTUBH. 51
CHAPTER V.
STRUCTURE.
Contents. — Parts of Transverse Framing, and How Combined and United
to Produce Greatest Pesistance to Alteration in Form — Sections of
Material Used — Compensation for Dispensing with Hold Beams — Parts
of Longitudinal Framing, How Combined and United to Transverse
Framing to Produce Greatest Resistance to all Kinds of Longitudinal
Bending and Twisting— Forms of Keels and Centre Keelsons, and their
Efficiency — Distribution of Material to Counteract Strain — Value of
Efficiently-Worked Shell and Deck Plating in Strengthening Ship
Girder — Definitions of Important Terms — Illustration of Growth of
Structural Strength, with Increase of Dimensions by means of Pro-
gressive Midship Sections — Special Strengthening in Machinery Space
— Methods of Supporting Aft End of Shafts in Twin- Screw Steamers —
Arrangements to Prevent Panting — Special Strengthening for Deck
Cargoes and Permanent Deck Weights, and also to Counteract Strains
due to Propulsion by wind — Types of Vessels — Comparison of Scant-
lings of a Three- Decked, a Spar- Decked, and an Awning-Decked Vessel
— Bulkheads — Rivets and Riveting.
Transverse Framing. — The parts of the structure of a ship
affording resistance to transverse strains, according to the usual
mode of construction, are included in the combination known as
transverse framing, A complete transverse frame comprises a
Jrame bar, a reverse bar, a floor ;plate, a beam, and a jjillar,
BOSOM PIECE.
BBHB
Section showing angle bar fitted to bosom
of frame and coveiing butt.
/BUTT
\ <^ BOSOM }^ PIECE » y
PLAN.
Fig. 37. — Angle Bar.
efficiently united. According to the size of the vessel, the
spacing of the transverse frames varies from about 20 to 26 *
inches from stem to stem. Let us take for our example an
ordinary merchant steamer, a midship section of which is shown
in fig. 36.
• A leading Liverpool Shipping Company is adopting a System of spacing
the Transverse frames 36 inches apart.
52
KNOW YOUR OWN SHIP.
SHELU
PUATINQ
^
FRAMC
B
FRAME
i^REVERSE
FRAM&
The frame har extends continuously from keel to gunwale in
this type of vessel. Should there,
from any cause, be a break in the
length of the frame, the strength
should be preserved by lapping the
parts to make the connection, or by
fitting angle butt straps, or other
efficient means of compensation should
be adopted (see fig. 37, and section
AB in fig. 36). This, indeed, is a
rule which should be rigorously ob-
served throughout the construction
of a ship, that wlierever a structural
part is weakened, the strength he fully
recovered hy compensation in some form
or other. If the frames meet or butt
on the keel, as they usually do, they
are connected by pieces of angle bar
about 3 feet long, fitted back to back,
which, in addition, provide a sub-
stantial means of connection to the
shell plating. The usual form of
frame is the plain angle bar (see A,
fig. 38^.
It will be noticed that one flange
of the bar is longer than the other ;
the long flange always points into
the interior of the ship, and the
short one is attached to the shell
plating. Since the greater the girth
of the vessel, and thus the greater
the collapsing strain, it is evident
that the vessel needs more transverse
strength in the region of midships,
where it is fullest, than towards the
ends. It is, therefore, usual to make
the frames one-twentieth of an inch
thicker for three-fifths of the length
at amidships than at the ends. The
frame bar is made stronger and more
rigid, and, therefore, the better able
to keep out the ship's side by means
of a reverse har, which is similar in
section, but smaller in size. It is
riveted to the back of the frame (see B, ^g, 38), and being
n
Fig. 38.— Fbame Bars.
STRUCTURE. 53
on the side of the frame hidden from view in fig. 36, it
is there shown in dotted lines. The reverse bar does not
always extend to the same height as the frame. As will be
seen further on, its height is governed by the tmnsverse dimen-
sions of the vessel, for the greater the girth and beam, the
greater the need for transverse strength. Across the bottom
of the ship, and extending well up the bilge, is a deep plate
called a floor plate. On the lower edge of this plate is attached
the large flange of the frame bar, and across the other side on
the upper edge is bent and riveted the reverse angle after it
leaves the frame (see section A B, ^g, 36). The floor plate,
being now converted into a girder, affords great stiffness and
strength to the bottom of the ship.
Instead of the usual frame and reverse frame there are other
sections of bar iron or steel which may be used. For example,
there is the Z-bar (see C, fig. 38), which is a combination of
the frame and reverse frame rolled in one section, thus saving
the necessity of riveting these two together. It is very strong,
and is extensively used in the building of ships for the Royal
Navy.
A very similar bar to this, sometimes used for framing large
vessels, is the channel iron section shown in D (fig. 38).
This also saves the riveting of a reverse bar. When this
section is used, it is generally dispensed with towards the ends
of the vessel, and the ordinary frame and reverse angle bar
substituted, as it is difficult to bend and bevel the channel bars
as required at the ends of the vessel. There is also the bulb
angle section (see E, ^g. 38).
This is sometimes adopted in vessels where no sparring is
required in the holds, thus permitting some kinds of cargo to be
trimmed right against the shell, an advantage being gained in
cubic capacity. By this means also the reverse bar may be
dispensed with when the bulb angle is made strong enough to
equal the frame and reverse bars together.
The beams form an important part of transverse framing, unit-
ing, as they do, the upper extremities of the frame bars and
holding them in position, thus forming the foundation for decks.
In addition, they complete the transverse section of the hollow
girder into which we have resolved our ship. It would be
useless to secure sufficient structural strength in the various
bars forming the transverse skeleton of a vessel, unless at the
same time every attention were given to the efficient connection
of these parts to one another. We have already noticed how
the frame butts are strengthened and connected, but there is
Btill the connection of the frame and the beams. This is done
54
KNOW YOUR OWN SHIP.
by welding or riveting to each extremity of the beam a hiee
2)laie (fig. 39), which is fitted into the bosom of the frame.
The British Corporation
recognises the necessity of an
efficient connection at this
part, by compelling all ships
built under its survey to have
knees three times the depth
of the beam, and one-and-
three-quarters the depth at
the throat, to all beams in
the way of the main deck.
Lloyd's require the depth of
the knee to be two-and-a-half
times the depth of the beam,
and one-and-a-half times the
depth of the beam at the
throat for steam vessels, while
for sailing ships over 36 feet
broad the knees must be
three times the depth of the
beam.
Like frame bars, the beams
may vary in sectional form.
Under iron or steel decks it
is usual and better to fit
angle or angle bulb beams
to every frame, and under
wood decks, on alternate
frames, beams of the following
sections may be adopted: —
(1) Butterly Bulb (see A,
fig. 40).
(2) Bulb Plate, and double
angles riveted to its upper edge (see B, fig. 40). Or,
(3) Channel Bar (see D, ^g, 38).
B A
Eleyatlon.
^
FRAMe
C:
BEAM
.
Plan.
Fig. 89.— Beam Knee.
Fig. 40. — Beams.
However, these forms may be considerably modified according
STRUCTURB.
55
to the length of the beams, since the length of the beams
determines the size of bar to be used. Vessels may have two,
three, four, or more tiers of beams, according to their depth.
Compensation for Dispensing with Hold Beams. — Now,
let us suppose a shipowner is about to have a vessel built with a
depth of 16 feet. He finds, if he intends to class the vessel at
Fig. 41. —Substitutes for Hold Beams,
Lloyd's, that she requires hold beams fastened to every tenth
frame, and at the extremities of the beams a stringer plate (see
^g, 36) securely attached to beams and shell. But as these
would interfere with the stowage of cargo he intends to carry,
let us see what alternative he may adopt in order to dispense
with the hold beams. If he wishes, he may fit transverse web
56 KNOW YOUR OWN SHIP.
frames (see fig. 41) at distances of eight frame spaces apart all
fore and aft ; this compensates for loss of beams.
In addition, there must be fitted a longitudinal web frame, or
web stringer as it is called, all fore and aft, between the trans-
verse web frames, and securely attached to them by angles on
the upper and the lower sides, and also by means of an efficient
diamond plate on its front edge. This compensates for the loss
of the stringer plate on hold beams. The next thing to be done
is to have the upper extremities of the web frames firmly tied
together and held in position. This is done by fitting extra
strong beams across the vessel, attached to the web frames by
extra strong deep knees. Since the function of the beam and
stringer plate is to tie and stiiffen the sides of the ship, the web
frame being a transverse plate girder, and the web stringer a
longitudinal plate girder, the one firmly united to the other
enables them to dp their work together, and thus serve the same
purpose. It will be observed that the web frame shown in fig.
41 is a continuation of the floor plate, and also that both it and
the web stringer are stiffened by double angles on their inner
edges.
Another alternative is to stiffen the ship at every frame space
all fore and aft by fitting together two large angles (as shown in
fig. 55). In conjunction with special hold stringers, this method,
known as "Deep Framing," makes a substitute for both hold
beams and reverse frames.
There is still another part in the transverse framing to be
noticed — viz., the 'pillars. They are riveted to the beams,
and usually to the girder on the top of the floors, or some other
part of the bottom of the vessel. They bind the upper and lower
parts of the structure together, and perform the function of a
strut and a tie by holding the beams and the bottom of the ship
in their right positions relatively to each other ; and thus by
uniting the two great horizontal flanges of the ship girder, the
deck and the bottom, they enable them to act in unison in
resisting longitudinal strains.
When considering the subject of strains, we noticed that in
rolling among waves a vessel has the tendency to alter her
transverse form, and to work at the comers. After observing
the combination constituting transverse framing, we shall now
be able to see how these parts unite in offering resistance to
the alteration of transverse form,
1. At the Bilge Corners. — Here we have the floor plate curved
np the bilge to a height of twice its depth at the middle line of
the vessel, thereby supporting the bilge in the form of a web at
every frame.
STBUCTUBB. 57
2, At tlie Deck Corners, — In this case we see the efficiency
developed by the deep beam knees in giving support in the form
of webs at every beam. Fig. 55 shows a similar web in a double-
bottomed vessel.
3. Furthermore, there is the great assistance provided in the
form of the beams themselves holding the sides of the vessel
rigid, the beams being in their turn supported by the pillars.
Longitudinal Framing. — The longitudinal framework of the
vessel is made up of the keel^ keelsons^ and stringers. These may
partake of a variety of forms, with a view of which we shall
briefly deal, together with the means adopted for binding them
all together in order to secure an efficient and strong framework.
The number of keelsons and stringers depends upon the size and
proportions of the vessel.
Keel, — ^The keel shown in fig, 36 is known as the ordinary bar
keel. It is made up of long lengths of bar iron connected by
means of scarphs, the length of which should be sufficient to secure
a good connection (see fig. 42). If the vessel be classed at Lloyd's,
CLCVATION OF K £ S L.
P LAN
Fig. 42. — Keel.
the scarphs will be nine times the thickness of the keel, and if
with the British Corporation, three times the depth of keel.
The same method of connection unites the keel to the stem
and the stem posts. These connections may also be made by
welding, but this is seldom done.
A superior arrangement of this kind of keel is the one known
as the side bar keel (see E, fig. 43).
It consists of a deep plate extending down from above the top
of the floors to the bottom of the keel, the thickness of the keel
part being made up by attaching two side bars or slabs of iron,
one on each side of the lower extremity of the centre plate.
The whole is then riveted to the two strakes of shell plating
which cover the keel, and are called the garhoard strakes (see
fig. 36). A thoroughly strong result is thus secured. Holes
58
KNOW TOUR OWN SHIP.
are cut in the centre plate at the top of the keel to allow the
Jieel jpiece, or frame back bar, as it is sometimes called, to be
fixed in position. The butts or connections of these plates com-
prising the keel must be kept well clear of each other, and
separated by at least two frame spaces, wherever practicable.
Fig. 43. — Keels and Keelsons op Vabious Forms.
The centre plate being carried up above the top of the floors
forms part of the centre keelson. Two horizontal plates are
then attached to the floor plates, one on each side of the centra
plate, the connection being made by means of the reverse angles.
To the upper edge of the centre keelson plate two angles are
STRUCTURB. 59
riveted, and also two others on the top of the horizontal plates.
The combination now forms a splendid backbone to the whole
ship. It will be noticed in ^g, 36, as also in A, B, C, D, and
E (fig. 43), that a short piece of angle bar called a lug piece is
attached to the top of the floors on the opposite side to the
reverse angle, thereby ensiwing a doubly strong connection
between the keelson and the transverse framing, for unless the
longitudinal and transverse framings are thoroughly united,
their separate strength is of little value to the ship as a whole,
and they would thus fail in their chief function.
Keelsons, — The commonest form of centre keelson consists of
a single plate standing upon the top of the floors with double
angles riveted to its upper and lower edges, as shown in B
(fig. 43). In addition, a plate called a rider plate is riveted on
the top of the two uppermost angles. The great disadvantage
of this keelson, especially in large, heavy vessels, is, that it
afibrds no resistance whatever to buckling of the floors, and
thus it has often happened that when vessels of this form of
construction have grounded upon an uneven bottom, the keel
has been sprung up, and consequently the floors having nothing
between them to stiffen them vertically at their deepest part,
have buckled. This lack of stiffening between floors is the
great defect of all keelsons standing simply upon the top of the
floors.
A very good kind of centre keelson is that shown in A
(fig. 43). Here we have the deficiency in the previous keelson
remedied. Its parts are as follows : — First, there is the deep
bulb plate, with angles on its lower edge, attached to the top of
the floors. Between one of the angles and the bulb plate an
intercostal plate is let down between all the floors on to the top
of the keel, and secured to the floors by vertical angle bars, as
shown.
A now unfamiliar, though very efficient, form of centre keelson
is sometimes to be seen in old vessels. A sketch of the same is
shown in C (fig. 43). It consists of a continuous centre plate
extending from the top of the floors to the top of the keel, the
latter being a broad, thick plate known as a flat-plate keel.
On the top of the floors a thick, broad plate is laid, and attached
to the vertical keelson plate by large, double, continuous angles,
as shown. Since the entire centre keelson is continuous, it
follows that the floor plates must butt on either side of it, the
connections between the two being made by double angles. The
vertical plates comprising the centre keelson are connected by
double butt straps (see fig. 73), treble riveted. The horizontal
plate is also riveted to the reverse angles on the top of the
60 KNOW TOUR OWN SHIP.
floors, and in addition to a short lug piece fitted on the top
edge of the floor opposite to the reverse bar. This form of
centre keelson is usually adopted in double bottoms (see
^g. 55).
In D (fig. 43) we have another modification of a centre keelson
with a flat plate keel. The centre plate is continuous, and
extends above the top of the floors sufficiently high to take two
large angle bars which are riveted to two horizontal plates
shown on each side of the centre plate, and also to the top of
the floors.
Keelsons and stringers are fitted for the purpose of giving
longitudinal stiffness to the vessel, and also in order to tie or
unite the transverse framing, so that, when strain is brought to
bear upon any particular part, it is transmitted to the structure
as a whole.
Keelsons and stringers are all forms of girders (see fig. 36),
varying both in number and size, according to the dimensions
and structural requirements of the vessel.
Those longitudinal stiffeners located along the bottom of the
vessel between bilge and bilge are called keelsons ; above the bilge
they are termed stringers.
Stringers. — It will be noticed that wherever a tier of beams
is fitted in a vessel, a broad, thick plate, called a stringer plate,
is attached to its extremities, and connected w^ith the shell by
a strong angle bar. This bar, called a sliell bar, is fitted inter-
costally between the frames if below the weather deck, and
to the reverse frames extending above the beams a continuous
angle bar is riveted, and also to the stringer plate. If the
deck is an iron or steel one, the plate at the end of the beams
is still called a stringer plate. It is always thicker than the
adjoining plating, and, being firmly connected with the beams
and shell, forms a splendid longitudinal stiffener to the vessel,
acting in conjunction with the beams and transverse framing in
keeping out the sides of the vessel to their proper position and
shape, and in resisting longitudinal twisting strains.
If the beams are widely spaced and no deck is laid, the stringer
plate is supported by means of knees or bracket plates under-
neath.
We observed at the beginning of this chapter that not only is
the transverse strain greatest, but the longitudinal also, in the
region amidships, and is gradually reduced towards the ends
of the vessel, thus showing that a reduction may be made in the
thickness of the material used in the construction towards the
ends. This applies generally throughout the vessel, for, be it
remembered, excessive strength is useless.
STRUCTURB. 61
Distribution of Material to Counteract Strain. — With
such an able means of conveying instruction to our minds as the
eye, it seems very probable that, with short explanatory notes,
a few sketches, showing both the arrangement and growth of the
framing and plating, ranging from the smallest to large types of
merchant vessels, will prove of more value, and will perhaps be
plainer than pages of printed matter. Before doing this we
must not omit to notice that although the first aim is to secure
the greatest possible efficiency by a judicious combination of
longitudinal and transverse framing, yet immense strength is
added by an efficiently worked skin, or shell plating, as it is
more commonly termed. Some parts of this outside plating are
capable of rendering more service to the structure than others.
For example, the ordinary bar, or hanging keel, as it is often
termed, has its only connection to the vessel by means of the
strakes, or rows of plating, called the garboard strakes, on either
side of the keel. The absurdity of connecting a thin plate to a
thick bar with large rivets, widely spaced, will be easily under-
stood, and thus the garboard strake is made thicker than its
adjacent plating. Moreover, where no heel pieces are fitted,
connecting the lower extremities or heels of the frames on one
side of the vessel to those on the other side, the garboard strakes
accomplish this by securing the heels of the frames firmly to
the top of the keeL It also adds stiffness to the bottom flange
of the ship girder.
We have already seen the advantage of strengthening the
upper and lower edges or flanges of a girder in increasing its
efficiency to resist longitudinal bending; and since a ship, as
previously stated, is simply a huge, hollow girder, any method
of deepening it vertically (ship's side plating, etc.), or increasing
the strength of its upper and lower flanges, must add to its
longitudinal strength. Hence it is compulsory, if a vessel be
classed, to have its uppermost strake of outside plating, called
the slieer strake, and sometimes the strake next below, increased
considerably in thickness (see ^g, 36). Also on the bottom of
the girder, in the region of the bilge, one or two of the strakes
are thickened in long vessels. Midway between the bilge and
the sheer strake — approximately in the region of the neutral
axis — where the strains vanish, the thickness of the plating is
least. The value of long bridges extending over the midship
length of a vessel, increasing the depth of the girder at the very
place where the bending strain is greatest, must be evident.
Indeed, in two- and three-decked vessels of over thirteen depths
to length, Lloyd's require that they have a substantial erection
extending over the midship half length. A complete or partial
62 KNOW YOUR OWN SHIP.
steel deck over the middle of the length, together with the
beams, also affords great strength to the ship girder in increasing
the efficiency of its upper flange.
Definition of Important Terms. — It is necessary at this
stage that a few terms be clearly understood.
1. Length between Perpendiculars, — For vessels with straight
stem this is taken from the fore part of the stem to the after
part of the stern post. Should the vessel have a clipper or
curved stem, the length is measured from the place where the
^^^ line of the upper deck beams would intersect the fore edge of
the stem, if it were produced in the same direction as the part
below the cutwater (fig. 44).
N,
Fio. 44. — Length between Perpendiculars.
2. " Lloyd's LengthJ' — Lloyd's length is the same as the fore-
going, except that the length is taken from the after side of the
stem to the fore side of the stern post.
3. Extreme Breadth, — This is measured over the outside
plating at the greatest breadth of the vessel.
4. Breadth Moulded. — This is taken over the frames at the
greatest breadth of the vessel.
5. Depth Moulded. — This is measured in one-, two-, and three-
deck vessels at the middle of the length from the top of the keel
to the top of the upper deck beams at the side of the vessel.
In spar- and awning-decked vessels, the depth moulded is
measured from the top of the keel to the top of the main deck
beams at the side of the vessel.
6. Lloyd's Depth. — This is somewhat different. We have seen
that they require a round up upon the weather decks, of a
STBUCTXTRB, 63
quarter of an inch to one foot of beam. This round up is added
to the moulded depth, and gives Lloyd's depth. "XVith this
modification it is otherwise the same as No. 5.
In designing our series of midship sections illustrating the
arrangement, amount, and development in structural strength
in progressive sizes of vessels, we will consider, for the sake of
example, that the vessels are to be classed at Lloyd's.
The size and spacing of all transverse framing — frames,
reverse frames, floor plates, pillars — are regulated by numbers
obtained entirely from transverse dimensions, as follows : —
Add together (measurements being taken in feet) half the
moulded breadth, tlie depth (Lloyd's), and the girth of tlie half
midship frame section of the vessel, measured from the centre
line at tlie top of tlie heel to tlie upper deck stringer plate. By
referring to the tables in Lloyd's rules, the sizes of these parts
of the structure, corresponding to the sum of these dimensions,
may be found. The number for three-deck steam vessels is pro-
duced by the dedu^ion of 7 feet from the sum of tlie measure-
ments taken to the top of tlie upper deck beams.
The sizes of all longitudinal framing — keel, keelsons, stringers,
as well as thickness of outside and deck plating, stem bar, and
stem frame — are governed by the number obtained by multiply^
ing Lloyd! s first number for frames, etc, by the length of the vessel.
Vessels of extreme dimensions require special stiffening above
that ordinarily needed by the numbers obtained as above, and
special provision is made for this in the rules.
64
KNOW TOUR OWN SHIP.
Under 13 feet depth. 12^ depths in length.
Fig. 45. —Dimensions of Framework and Plating fob
Vessels less than 13 feet in depth.
i Girth, .
I Breadth,
Depth, .
Lloyd's Numerals.
1st No.,
Length,
2nd No.,
21-8
120
12-88
46'C3
161
7507
Frames, 3 x 3 x , spaced 21 ins.
Reverse frames, 2J x 2J x ^f^.
Floors, 13 X ^ ~ ^
20
Centre keelson, 11 x
9-7
"20~'
Keelson continuous angles, ZixZx-^Q,
Beams, 5J x ^ - bulb plate with
Double angles, 2^ x 2^ x ^.
Sheer strake, 32 x -^-^ ~ ^
Garboard strake, 31 x
20 ■
9-8
"20"'
Stringer plate, 36 x -^^y - 19 x ■^.
Gunwale angle bar, 8 x 8 x |^.
Keel, 7 x If.
Additions for Extreme Length,
To thickness of sheer strake, ^ is added for | L amidships.
To bilge keelson, a bulb plate is added for f L amidships.
To thickness of 2 strakes at bilge, -^ is added for } L amidships.
Abbreviations.
L means length, thus
} L amidships ,, three-fourths length amidships.
R „ reserve frame height.
8-7
20
II
thickness reduced from ^ to ^.
Note, — All sizes of plates and angle bars are given in inches.
STBUCTUBE.
05
Under 14 feet depth. 12^ depths in length.
Fio. 46. — Dimensions op Framework and Plating for
Vessels less than 14 feet in depth.
Lloyd's Numerals.
i Girth, .
I Breadth,
Depth, .
1st No.,
Length,
24
13-5
13-83
51-33
173
2nd No., 8880
6 - 5 ■
Frames, 3 x 3 x
20
., spaced 21 inches.
Reverse frames, 2^ x 2} x ^.
Floors, 14i X ^ " ^
20
Centre keelson, 12 x
9-7
20 •
Keelson continuous angles, 3^ x 3 x -^V
Hold pillars, 2^.
Sheer strake, 33 x "^^
Garboard strake, 32 x
20
9-8
20
Deck stringer plate, 38 x ^^ - 20 x ,%.
Gunwale angle bar, 3 x 8 x ^.
Keel, 7J x IJ.
Additions for Extreme Length,
To thickness of sheer strake, -^ is added for | L amidships.
To bilge keelson, a bulb plate is added for f L amidships.
To thickness of 2 strakes at bilge, ^ is added for i L amidships.
B
66
KNOW TOUR OWN SHIP.
^ MX i I II I ■ ■■II I II I I p oxg
lea
Under 16^ feet depth. 12} depths in length.
Fig. 47.— Dimensions op Framework and Plating Foa
Vessels less than 15} feet in i>epth.
Iiloyd's Numerals.
i Girth 26'5
I Breadth, 14*5
Depth, 16-33
1st No.,
Length,
2nd No.
66-33
192
. 10816
6-5
Frames, 3J x 3 x — — — , spaced 22 inches.
Reverse frames, 2 x 2^ x ^q.
Floors, 16 X ^ " ^
20 •
Centre keelson, 12 x
10-8
20 •
Keelson continuous angles, 4^ x 3 x /q.
Hold pillars, 2f .
Beams 7 x ^, " bulb plate with | ^^^^^
Double angles, Z x B x J^^ J *"»'^*"»«'« "»*"«*
Sheer strake, 34 x ^^ " ^
Garboard strake, 32 x
20
9-8
~20"'
Deck stringer plate, 40 x -^jj - 22 x /^y.
Gunwale angle bar, 3^ x 3| x Z^.
Keel, 7i x 2.
Additions for Extreme Length,
To thickness of sheer strake, -^ is added for | L amidships.
To strake below sheer strake, 4is is added for ^ L amidships.
To bilge keelson, a bulb plate is added for f L amidships.
To thickness of 2 strakes at bilge, ^ is added for i L amidships.
67
Under 16} feet depth. 12} depths in length.
FiQ. 48. — DiMBNSiONS OF Frambwoek and Plating fob
Ybssbls lbss than 16i fbbt in dbfth.
Iiloyd's Numerals.
i Girth, 28-3
i Breadth, 15*5
Depth, . . . . . . . 16-33
1st No.,
Length,
60-13
205
2nd No 12326
7 — 6
Frames, 3} x 3 x 1 r, spaced 22 inches.
Beverse frames, 3 x 2^ x |/\).
Floors, 17i X ^ " ^
20
Centre keelson, 13 x
10-8
Keelson continuous angles, 4} x 3} x -f^.
Main deck beams, 7i x A, bulb plate with \ -Uemate frames
Double angles, 3 x 3 x A J ^^^^^^^^ "*'"®^-
Hold beams, 8 J x -^^ bulb plate with \ on every 10th
Double angles, 4 x 3 x /o, with covering plate J frame.
Main deck stringer plate, 44 x ^ - 24 x j^.
Hold stringer plate, 27 x -^ - 21 x A.
Gunwale angle bar, 4 x 4 x -A.
Sheer strake, 36 x ^^ ~ ^
Garboard strake, 33 x
20
10-9
"■20"'
Keel, 7J x 2J.
Hold pillars, 2|.
Additions for Extreme Length,
To thickness of sheer strake, ^ is added for | L amidships.
To strake below sheer strake, -^ is added for ^ L amidships.
To bilge keelson, a bulb plate is added for ^ L amidships.
To thickness of 2 strakes at bilge, ^ is added for ( L amidships.
68
KNOW YOITB OWN SHIP.
Under 23 feet depth. 12^ depths in length.
Fig. 49.— Dimensions of Framework and Plating foe Vessels
LESS than 23 FEET IN DEPTH.
STBUCTURB. 69
liloyd^s Numerals.
J Girth .88
I Breadth, 19
Depth, 22*83
1st No., 79-83
Length 286
2nd No., 22831
8 — 7
Frames, 5 x 3 x , spaced 24 inches.
Reverse frames, 3^ x 3 x ^7.
Floors, 24 x l^-ZA.
' 20
to _ It
Centre keelson, 20 x i^ —,
20
Keelson continuous angles, 6 x 4 x /^«
Intercostal keelson plate, •^«
Complete steel deck, ^ thick on main deck.
9 — 8
Main deck heams, 6^ x 3 x , bulb angle on every frame.
Hold beams, 10 J x ^ bulb plate, with \ ^verv 10th frama.
Double angles, 4i x 4 x ^% r^ ®^®^^ ^^'^ "^^^
Main deck stringer plate, 41 x ^ - 35 x ^,
Hold stringer plate, 38 x -^ - 29 x ^fy.
Gunwale angle bar, 4^ x 4^ x ^.
Sheer strake, 42 x ^^ ~ "^^^
' 20
12 — 11
Garboard strake, 36 x — — — ^
Eeel, 10 X 2}.
Hold pillars, 3^.
Additions for Extreme Length,
To thickness of sheer strake, ^^ is added for | L amidships.
To strake below sheer strake, ^^ is added for ^ L amidships.
To bilge keelson, a bulb plate is added for f L amidships.
To thickness of 3 strakes at bilge, -j^ is added for J L amidships.
70
KNOW TOUR OWN SHIP.
Under 26 feet depth.
16 depths to middle deck in length.
11*6 „ upper
II
FiQ. 50.— DiBfBNSiONS OP Pramework and Plating for Vessels
LESS THAN 26 FEET IN DEPTH.
STRUCTURE. 71
Lloyd's Numerals.
i Girth, 4075
* Breadth, 20*5
Depth, 25-83
87-08
7
1st No., 8008
Length, 301
2nd No., 24104
8 — 7
Frames, 5 x 3J x ■ spaced 24 inches.
Reverse frames, 3} x 3^ x ^^.
Floors, 24J x ^^^^T^.
Centre keelson, 25 x — - — •
20
Keelson continuous angles, 6^ x 4 x ^V
Intercostal keelson plate, ^.
Complete steel deck, ^ thick on main deck.
10 — 9
Upper deck heams, 7J x 3 x — — - — bulb angles on every frame.
^\)
Middle deck beams, 10 x ^J, bulb plate with Ion every alternate
Double angles, 3^ x 3i x ^ / frame.
Hold beams, 11 x ^, bulb plate with J . ., -
Double angles, 5x4x3^ { °" ®^®^y ^®^^^ "*"^®-
Upper deck stringer plate, 43 x ^^ - 36 x ^^.
Miadle deck stringer plate, 62 x ^ - 36 x -^q.
Hold stringer plate, 40 x ^^ - 31 x ^.
Gunwale angle bar, 4^ x 4^ x 1%,
Sheer strake, 42 x — - — .
' 20
12 — 11
Garboard strake, 36 x i__ ^_.
* 20
Keel, 10 X 2f.
Hold pillars, 3|.
Additions for Extreme Length.
To thickness of sheer strake, ^ is added for | L amidships.
To bilge keelson, a bulb plate is added for f L amidships, and
an intercostal plate for J L amidships.
To thickness of 2 strakes at bilge, -^ is added all fore and aft.
Centre keelson increased in depth.
To side keelson, a bulb is added for i L amidships.
To bilge stringer, an intercostal plate is added for | L amidships.
72
KNOW TOUR OWN SHIP.
Under 86 feet depth (also nnder S9 feet).
15*5 depths to middle deck In length.
12 '5 ,f upper „
Fia. 51. — Dimensions of Framework for Vessels less than
36 FEET IN depth.
Note.— The scantlings are for the vessel nnder 36 feet depth, all of which are shown in
clear, black lines. The tig. is drawn to the under S9 feet depth in order to show the
introduction of the new tier of beams indicated by dotted lines. Such a Teasel would
rec^uire both additional topside and bottom strengthening.
STRUCTURB. 73
Lloyd's Numerals.
_ Girth, 62-6
* Breadth, 25
Depth, 85*83
113-33
7
IstKo., . 106-33
Length, 448
2nd No., 47635
Frames, 6 x 34 x ~ , spaced 25 inches.
Reverse frames, 4} x 3^ x ^^.
Floors, 32 x l ^' ^ .
* 20
Centre keelson, 36 x ~ .
* 20
Keelson continuous angles, 6^ x 4| x ^.
Intercostal keelson plates, ^.
Foundation plate, 18 x \%,
Complete steel deck to upper deck, -j^^.
Complete steel deck to middle deck, •^.
12 — 11
Upper deck beams, 9 x 3 x — Kfr—> ^^^ angle on every frame.
12 — 11
Middle deck beams, 9 x 3 x — , bulb angle on every frame.
Lower deck beams, 12 x ^, with \ ^^ ^„«.^ o^a Aw.*»<>
Double angles, k x 3 J x ^ T^ ^^^^ ^^^ ^^"'^
Upper deck stringer plate, 64 x ^ - 51 x ^.
Miadle deck stringer plate, 64 x ^ - 51 x ^V
Lower deck stringer plate, 56 x ^ - 44 x A.
Gunwale angle bar, 5 x 5 x ^^.
Sheer strake, 46 x i^^— .
' 20
Garboard strake, 36 x _~ _.
20
Keel, 12 x 3J.
Hold pillars, 4.
Additions for Extreme Length.
Sheer strake doubled for whole width, for f L amidships.
To strake below sheer strake, -^ is added for L amidships.
To upper deck stringer plate, -^ is added for f L amidships.
To side keelson, continuous plate is added for f L amidships.
To bilge keelson, continuous plate is added for ^ L amidships.
To bilge stringer, intercostal plate is added for | L amidships.
Centre keelson increased in depth.
74 KNOW YOUB OWN SHIP.
Relation of Strength to Dimensions — Notes on "Mid-
ship Sections.** — In considering the subject of strains, it was
found that both longitudinal and transverse strains decreased
towards the ends of the vessel, being greatest on each side of mid-
ships. Naturally, therefore, in turning to the transverse sections
(figs. 45 to 51), we expect to find a corresponding arrangement
of structural strength. Such, indeed, is the case. In the trans-
verse framing the frames and floors maintain their maximum
size for three-fifths of the vessel's length amidships, and are
reduced in thickness for the remaining one-fifth of the length
at each end. The floors are carried up the bilge to a height of
twice their midship depth above the top of the keel, for one-
fourth of the midship length of the vessel. Fore and aft of this
distance, the ends are gradually lowered until the tops of the
floors are level. At the extreme ends, however, the floors are
increased in depth, as subsequently shown.
The height to which the reverse frames are carried varies
according to the transverse dimensions of the vessel. When
Lloyd's first number is below 45, the reverse frames are carried
across every floor plate, and up the frame to the upper part of
the bilges ; when 45 and below 57 they extend alternately to
the gunwale, and high enough to enable the double angle
stringer above the bilges to be securely connected; or, if hold
beams are fitted, high enough to get a good connection to the
beam stringer angle. When the number is 57 and above, the
reverse frames extend alternately to the gunwale and the
stringer next below. When the number for sailing vessels
reaches or exceeds 75, the reverse frames extend to the gun-
wale on every frame.
Except in spar- and awning-decked vessels, and in poops and
forecastles, the beams, exclusive of hold beams, where less than
three-fourths the length of the midship beam, are somewhat
reduced — in many cases — in both depth and thickness.
In the vessels of which figs. 45, 46, and 47 are midship
sections, only one tier of beams is required; but immediately
the depth reaches and exceeds 15 feet 6 inches (Lloyd's depth),
a tier of widely-spaced hold beams is fitted (figs. 48 and 49),
with a continuous stringer plate on the ends. This, together
with the gradual growth of the other framing, provides the
additional transverse and longitudinal strength demanded by
greater depth and length. When 24 feet is reached and
exceeded, another tier of beams is required (fig. 50).
When the depth reaches 32 feet 6 inches, although another
tier of beams is not required, a stringer plate supported on
alternate frames by large bracket knees has to be fitted, and on
STRUCTITRB. .75
its inner edge is riveted a large angle of the size of the centre
keelson angles, converting it still further into an efficient girder.
"When 36 feet depth is reached, the additions shown by the
dotted lines in fig. 51 are required. Here we have a fourth
tier of beams of extra strength fitted to every tenth frame.
These are known as orlop beams.
Turning to the longitudinal framework, we find similar reduc-
tions in the scantlings taking place. The centre keelson plate
standing upon the top of the floors, together with its rider plate,
maintains the midship thickness for (me-half the vessel's length
amidships. Beyond this length considerable reduction takes
place in the thickness, and the rider plate disappears altogether
before and abaft of the three-fourths length amidships. Stringer
plates at the ends of beams retain their midship dimension for
one-half the vessel's length. Throughout the remaining one-
fourth length at each end they gradually diminish in both
breadth and thickness. The number of hold stringers and
keelsons to below the bilge is regulated entirely by the depth
of the vessel. The sizes of all the large angles for keelsons and
stringers in the hold are the same as the centre keelson angles.
A glance at the outside shell plating covering the frames also
shows a reduction, and this takes place on the one-fourth length
at each end.
Where a steel deck of seven-twentieths of an inch or over is
fitted, it is reduced in thickness fore and aft of the half length
amidships. A little consideration will soon make it obvious
that it would be absurd to deal out to every vessel of similar
" 2nd numerals " exactly similar longitudinal strengthening, for
then a long, shallow vessel would receive actually less longi-
tudinal stiffening than a shorter, deep one, since the introduc-
tion of hold stringers and keelsons is regulated almost entirely
by the depth.
We have already seen that long, shallow vessels with small
depth of girder possess less resistance to bending than shorter
ones, not to mention shorter and deeper vessels. It is, there-
fore, the custom with classifying associations to ^^ upon a
standard vessel of a certain number of depths to the length.
Lloyd's Committee adopt a length of eleven depths as the
standard worked upon. Vessels exceeding these proportions
are, therefore, subject to the introduction of additional longi-
tudinal strengthening over the middle of the length. In figs.
45 to 51, the number of depths in length is 12*5, excepting fig.
50, which is 11-6, and the additional strengthening therefore
required is shown, as far as possible, on their respective
sketches, as well as in the table of additions on each diagram.
76 KNOW YOUB OWN SHIP.
When in three-decked vessels the length is more than eleven
times the depth taken from the top of the keel to the top of the
middle deck beams, special additional strength has to be introduced
at the bilge and bottom. Such strength has been introduced
into the foregoing midship sections. All vessels having a length
of thirteen or more times the depth from the top of the keel to
the top of the upper deck beams are to have a substantial erec-
tion, such as a bridge, extending over the half length of the
vessel amidships.
A perusal of figs. 45 to 51, with the scantlings accompanying
them, will, it is believed, fully verify the foregoing remarks upon
the arrangement and growth of structural strength.
Local Strengthening — Space occupied by Machinery. —
Engine and Boiler Space, — Perhaps one of the first things which
strikes one in studying the arrangement of a steam vessel, from
a structural point of view, is the concentration of weight, and
also the vibration, especially in vessels of high speed, in the
machinery space. In addition to this, there is a break in the
arrangement of transverse strength owing to the omission of
beams, and even at the upper deck the beams are cut in the way
of the engine and boiler casings. The result of all this is to
produce a tendency to vertical elongation, and to cause the
upper breadth of the vessel to contract.
Moreover, if the vessel did not possess sufficient rigidity and
stiffness to resist working under the vibration of the engines,
the evil would rapidly increase, and assume serious dimensions.
But, happily, all this can be provided against, and although the
methods adopted may vary somewhat for different types of
vessels, yet a few general hints may be given.
First of all, a good foundation must be secured for both'
engines and boilers. Lloyd's require that floor plates under
engines be one-twentieth of an inch thicker, and under boilers
two-twentieths of an inch thicker than are otherwise required,
and by this means greater stiffness is given to the bottom of the
vessel. No doubt the extra one-twentieth put upon boiler
floors is on account of the fact that the damp heat created there
has the effect of making corrosion more rapid than elsewhere.
At the same time, it should be noted that a great deal of the
corrosion in this locality is due to neglect, for if the bottoms of
vessels were carefully watched, and frequently cement washed,
there would be less cause for complaint regarding the condition
of the floors of comparatively new vessels, and it would be found
that a little care is cheaper in the end than new floors. As a
rule, it is found, in vessels with ordinary floors, that the engine
foundation or seat, as it is more commonly called, has to be built,
Engine seat.
77
Blevatioib
SHCt-k.
flan.
Section.
Fig. 52.— Engine Seat.
I
78
KNOW YOUB OWN SHIP.
to a height considerably above the floors. When this is the case,
and it is practicable, a splendid seat is constructed by making the
floors deep enough to reach to the engine seat, and to extend with
horizontal edges from side to side of the vessel. Across the top of
all floors in engine and boiler space, Lloyd's require double reverse
angles to be fitted at least from bilge to bilge. This not only
stiffens the floor, but forms a good means of connection for the
thick plating to which the bed plate of the engine is bolted.
Intercostal plates, fitted between floors, on either side of the
FiQ. 53. — ^Tbotjgh ttndeb Engines to catch Grease Drip.
centre line, give further stifihess to the floors, and support for the
condenser, etc. (see fig. 52).
Sometimes, especially in the case of yachts, a watertight trough
is fitted in the engine floors immediately under the shafting,
which prevents the grease drip from the engine finding its way
into the bilges (fig. 53).
Where the floors are not made continuous from keel to engine
seat, and from bilge to bilge, a seat has to be built simply in the
way of the engine on the top of the ordinary floors; this, however,
lacks in efficiency as compared with the previous method.
The boilers, too, require to be fitted on foundations which are
firm and rigid, and securely connected with the bottom of the
vessel (fig. 54). This is done by fixing two or three thick plates
called stools^ to the top of the floor plates under each boiler. The
STRUCTURE.
79
top edges of these plates are cut to shape so as to receive the
boiler. They are attached to the double reverse angles on the
top of the floors by means of double angles, and roimd thehr edges
are fitted large double angles. These provide a good surface
upon which the boiler can rest. Then, to hold the stools in place
and prevent them tripping— that is, inclining one way or
another— tie ])lates are fitted fore and aft, and connected to the
double angles. In the case of vessels constructed with double
bottoms, for water ballast, as shown in fig. 55, the engines
generally stand upon the tank top, this usually being of sufficient
height. Sometimes, however, it is necessary to build a girder seat
upon the inner bottom plating, in order to raise the engines to the
desired height In any case, the inner bottom plating is increased
Fio. 64.— Boiler Stool.
in thickness in way of the engine and boiler space, and immediately
under the engines a thick foundation plate is firmly riveted.
This plate may form a part of the inner bottom plating, or may be
riveted on the top of the inner bottom plating when the engines
stand immediately upon the tank top, or it may be riveted to the
top of the girder seating when such an arrangement exists. To
this the bed plate of the engine is bolted. The boiler stools are
riveted to the inner bottom plating. As in the case of ordinary
floors, extra stiflening is required at the bottom of the vessel
under the engines and boilers, and this is done by fitting inter-
costal girders.
Having stiffened the bottom of the ship, it is necessary to
provide for the loss of the beams, and also some means of keeping
out the sides of the vessel This is done in exactly the same
80
KNOW YOUB OWN SHIP.
manner as when hold beams are dispensed with — viz., web frames
are fitted. In high speed vessels especially, care should be tak^n
that sufficient of these are introduced. Valuable as web stringers
are, in conjunction with web frames, it is found better in the
Fig. 55. — Midship Section of a Vbssbl built on the "Deep Fsams"
Ststem with a Cellulab Double Bottom.
machinery space to fit extra strong beams wherever practicable.
Several forms may be adopted, according to the size of the vessel
(see B, C, D, E and F, fig. 32).
It will often be found of advantage to further stiffen the frames
in the engine and boiler space by fitting all the reverse angles to
STRUCTURE.
81
the upper deck, and in some cases the double reverse bars
also.
Sometimes in vessels with the centre keelson fitted on the top
of the ordinary floors (fig. 56), the height of the keelson throws
FUKTtL -
Intercostal plates shown by crossed, dotted lines.
Fig. 66. — Intercostal Compensation fob Reduction in Depth
OF Centre Keelson under Boilers.
the boiler or boilers too high, and it is necessary to cut the keelson
down. Were no compensation made for this reduction in the
height of the girder, the weakness at this part would be a most
serious defect. Several means, however, may be adopted to recover
the strength.
In the first place, it will be seen that, owing to the depth of
the keelson being reduced, the sectional area of the keelson is
reduced also. This may be recovered by making the central plate
thicker at this part until the sectional area has been regained.
But even this does not fully recover the loss of strength, for
though the sectional area is obtained, yet the reduced depth of
the girder proves a loss of strength in resisting longitudinal bending.
It, therefore, becomes necessary to increase the sectional area to
beyond what it was in its original condition. A good method of
compensation is to fit intercostal plates between the floois, and
attached to the centre plate by means of its lower angles, as shown
in fig. 56.
Again, it sometimes happens that, in the way of the boilers,
it is necessary to reduce the width of the hold stringer plates.
Compensation may be made, as in keelsons, by increasing the
thickness of the plate in the way of the reduced width, and also
by fitting strong angles on the inner edge of the stringer plate.
Mode of Strengthening Ship at Aft End of Shafting. —
Leaving the engine and boiler space, and travelling aft, great
vibration and strain is thrown upon the vessel, especially when
in a seaway, by the action of the propeller. At one moment it is
F
82 KNOW YOUR OWN SHIP.
totally submerged, and revolves with regular precision, but imme-
diately after the wave has passed, it is totally or partly out of the
water, and races at a high speed. Provision must, therefore, be
made for this. To stiffen the sides of the vessel, the floor plates
at the aft end should be made considerably deeper, and towards
the stern post they should be carried above the shaft, so that the
shaft passes through them. Then, again, it is most important
that a sound connection be made between the outside plating and
the stern post. By the midship sections we see that considerable
reduction takes place in the thickness of the end outside plating.
To connect thin plating to a massive iron stern post with large
rivets widely spaced would, it is likely, result in the thin plate
being unable to hold the stem post rigid under the strains men-
tioned, and leakage would ensue. So what is done is to increase
the thickness of these endmost plates to at least the thickness of
the plating at midships, and thereby get a more evenly balanced
connection.
But a further means of rigidly fixing the stem frame is re-
quired, and this is done by fitting a deep plate, called a transome
plate, against the upper part of the stern post, extending across
the counter from side to side, and riveted to the frames. The
connection between the stem post and the transome plate is
effected by means of strong angles (see fig. 57, section A B).
It is well known to seamen that considerable leakage often
takes place, notwithstanding these precautions to hold the post
fixed. An additional means to secure this end is to have another
post carried up at the fore side of the stern frame (Y in sketch),
and this also is attached to a stout plate carried from side to
side of the vessel, and connected with the frames as well as to
a bracket plate at the lower deck. By this method, with sound
workmanship, and by filling in the space above the propeller
aperture between the two parts with cement, leakage is very
improbable.
In the case of steamers with twin screws, a different arrange-
ment of supporting the end shafting has to be adopted. One
method, after leaving the skin of the ship, is by projecting struts,
as shown in fig. 58.
The importance of having these struts securely attached to the
hull of the vessel will readily be observed, for should any accident
happen here, the vessel is entirely crippled. When the screws
somewhat overlap each other, and revolve partly in an aperture
in the stern frame, a sound and reliable connection of the struts
with the stern frame may be made, as shown by fig. 58, a and 6,
the ends of the struts being welded out into broad palms capable
of taking a sufi&cient number of rivets. If there is a weak point
STRUCTURE.
83
in this method, it is in the fact that both the upper palms of the
struts, and also the lower palms, are connected by the same rivets,
so that on each side of the main post, owing to the vibration of
the shafts, there is this tendency to work or shear the rivets.
Each rivet, therefore, bears a double strain. But where no aper-
ture is needed for the propellers, the shell plating is carried out
to the after stern post, and another means has to be provided for
the connection of the struts. The commonest way, perhaps, is
that shown in fig. 59.
Here the upper palms are simply fixed on to the outside shell
/DECKi
"^braCkkt PLATR
CONNECTING POST
TO OCCKBCAM
SECTION A.e. £NLARCED
RUDDER POSr
8TERN POST
RUDDER
TRUNK
TRANSOMS PLATCi
TffANSOME
PLATE
LOWER D?
BRACKET PLATE'
8CARPH
ENLARGED
(/ VIEW AtY
LOOKING APT
Fio. 57.— Ste&n F&ame and Connecxiun.
plating. If this were all the connection, it would not take a keen
observer to see that the immense vibration of the shafting, especi-
ally in high-speed steamers, would simply tear away the plating.
It therefore becomes absolutely essential that the most effectual
means be adopted to secure the best and surest connection. Two
things have to be aimed at in accomplishing this. First, that at
the point where the shafts emerge from the hull, the vessel be
well stiffened and bound together, so as to reduce the vibration to
a minimum ; and second, that in the way of the strut connections
the ship be well strengthened. A variety of means may be used
84
KNOW YOUR OWN SHIP.
^eCTlOHTKROUCII
.A. B.
n
SHCLL
PLATINQl
/
PAL^nS FOR
STBVTS
STRUT
(a) Elevation.
(b) Transverse Section.
Fig. 58.— CoNiTECTiON of Struts with Stern Frame in Twin-screw
Steamers — a, Elevation; b, Transverse Section.
BTBUCTUBB. 8S
to attain the former of these. For example, in some veBsels the
method shotca in fig. 69 might be eanied out.
Here a very thick plate or neb is placed across the ehip from
side to side, and securely riveted to the main frames (A in fig.
60). Through this plate the shafts pass. If the vessel be not
too vide at this part, this alone will form an efficient tie to the
two sides, and give the required stifiness. However, in larger
vessels, where the screws are further apart, it would be necessary
r ' pl«t-*--»»>
:^
tUEVATtON
to further stiffen this web by means of angle bars or bulb angles
across its face, or even introduce more of these web plates on
adjacent frames.
in way of the struts, the following system might be em-
ployed : —
1. Carry up all the floor plates from the stem post, to a few
frames forward of the struts, above the height of the upper palms
(«ee fig: 69).
86
KNOW YOUR OWN SHIP,
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"A
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O
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to
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BTRUCTURB. 87
2. If possible, arrange for a double frame on each side of the
vessel to come in the centre of the palms, having thick, broad
flanges against the outside plating.
3. If the strake of plating, upon which the palms of the struts
rest, be an outside one, fit a doubling plate between the edges of
the two adjacent strakes, extending fore and aft from the after side
of the frame abaft to the fore side of the frame before the double
frame angles.
If the strake of plating be an inside one, the doubling plate
may be fitted on the outside of the shell plating. With this
additional strengthening, the palms can now be securely attached
to the plating with rivets, through the shell plating, doubling
plate, and large double-frame angles. Athwartship, the vessel
is strengthened by the deep floor plates already mentioned.
In any case, in steam vessels there would be a watertight
bulkhead at some little distance forward of the struts. But
where in such vessels as these there is the greater possibility of
leakage, it would be well to construct a watertight flat at a small
height above the upper palms of the struts, so that, if leakage did
occur, only this compartment would be flooded. From this
bulkhead, it would also be well to continue the watertight flat
just above the shafting, and extend it far enough forward to
include the point where the shafts emerge from the shell, since
this is another place where leakage might take place (A in fig. 59).
This method of strut connection has the advantage of having
the strain of the vibration of only one of the shafts thrown upon
the rivets connecting the palms with the hull, each upper palm
being a separate connection.
Another method of strut connection is that shown in fig. 60, a
and h.
In this case, the struts are carried through the outside plating,
and attached to a very thick intercostal plate, fitted between thick
transverse plates. To insure watertightness where the struts
pierce the shell, collars would have to be wrought and carefully
caulked ; and the chambers into which the struts enter should be
made watertight also. This method has the same disadvantage
mentioned in fig. 58 — viz., the same rivets connect both palms.
A system has been adopted in recent years of supporting the
end shafting in large twin-screw vessels, on first leaving the main
body of the hull, by carrying out the framing and shell plating
round the shafting. Further aft, however, where the shaft is con-
siderably out from the hull, the main frame is carried down in
the usual way (fig. 61), and a piece of frame bar is scarphed on
to the main frame, which, together with the shell-plating, is
worked round the shaft, binding the projection to, and, indeed,
88
KNOW YOUR OWN SHIP.
making it an integral part of the structure. By this method the.
struts are dispensed with, and a strong and efficient means of
supporting the shafting is obtained.
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^^^ WATERTICMT CKAMB£Rfll
Enlarged plan of fig. 60, &
Fig. 60, 6. —Struts cabbiet) through Shell Plating into
Watertight Chamber (Plan).
Panting. — Several means may be adopted to prevent panting,
a few of which we shall notice. The common method is to fit
plate stringers, called 'panting stringers^ in addition to the ordinary
STRUCTURBL
89
stringers of the vessel, extending from abaft the collision bulk-
head continuously into the stem, where they are joined by means
of a plate called a breast hook, uniting, as it were, the two breasts
of the vessel. These stringer plates are supported on beams, as
shown in fig. 62.
An objection raised against this method of stiffening is that it
forms an isolated rigid girder
and the vessel is inclined to fall
hollow on each side of it, especi-
ally if subject to encountering
ice, as in the Baltic at certain
seasons. What is wanted is
a more even distribution of
strength. This may be obtained
by a slight modification in the
arrangement of the transverse
framing. The usual practice is
to space the frames of a vessel
throughout the length at equal
distances apart, and measured in
a fore and aft direction on the
top of the keel. Let the frame
spacing, as required by Lloyd's,
be 24 inches. While the dis-
tance from heel to heel of the
respective frames may measure
exactly 24 inches as they stand
upon the keel, yet, especially in
very bluff-ended vessels, at water-
planes above the keel, where the
shell rapidly curves in to the
stem and stem, it may be found
that the frame spacing measures
as much as 26 inches — actually
further apart than at amidships. Figures 62 and 63, which
represent a somewhat fine-ended vessel, will, however, illustrate
this. To give stiffness to the fore end, the frames should be spaced
rather more closely instead of more widely, so as to produce, say
2 or 3 inches less than Lloyd's requirements when measured on
the shell. It will also be found of advantage to increase the thick-
ness of the shell plating. Whatever method be adopted, it is advis-
able to considerably increase the depth of the fore end floors.
The introduction of a few extra beams with stringer plates on
their ends, where the ordinary stringers are widely spaced, will
generally give sufficient stiffness.
Fig. 61.— Method of nisrENsiNa
WITH Struts in Twin- Screw
Steamers.
KKOW sons OWN SHIP.
Fio. 63— Plas op Pabtikq Smixci
STRUCTURE. 91
Deck Cargoes and Permanent Deck Weights. — To pro-
vide against the strain caused by the weight of heavy timber or
other deck cargoes, the important point to be observed is that
the beams are held rigidly in place at their centres ; it is only
when the deck sinks at the centre that any damage can be
wrought upon the beam knees. Therefore, to provide efficiently
against these strains, extra strong stanchions should be fitted under
the beams, with well-formed heads, and spaced not more than two
frame spaces apart. Where heavy permanent weights are carried
on the deck, such as winches, windlass, etc., local strength may be
obtained by fitting extra strong beams supported by additional
pillars.
Strains from Masts due to Propulsion by Wind. — The
important point to be aimed at in this case is to transmit, especi-
ally in the case of vessels propelled wholly by wind, the immense
strain which is thrown on to the hull, so as to make it as general
as possible, though it is classed as a local one. This is accom-
plished by making good three conditions —
1. That the heel or lowest extremity of the mast be firmly
secured and rendered immovable. If the mast is stepped on the
top of a centre keelson, the heel may be secured as shown in ^g.
64, a thick plate being firmly attached to the top of the centre
keelson, with a circular, welded bulb angle well riveted on its
upper face, into which the heel of the mast is stepped and firmly
wedged. The mast is prevented from working at its lower
extremity by means of a piece of T-bar riveted to the centre
keelson, and notched into the mast heel.
2. That the mast be thoroughly secured at the upper deck.
Since a great part of the strain is encountered here, it follows
that the means to counteract it should be most efficient. If the
deck is plated with iron or steel, and the plate in way of the mast
is of reasonable thickness, a stout, circular, welded angle bulb to
receive the wedging round the mast at the deck will provide a
satisfactory means of transmitting the strain to the deck as a
whole. Should, however, the deck not be entirely plated, a stout
I)late, called a mast partner, should be attached to the beams
round the mast, which in its turn should be efficiently attached
to the neighbouring beams and stringer plates by tie plates, as
shown in fig. 65. In this way, again, the strain is transmitted
to the deck as a whole.
3. That the upper reaches of the mast be held firm, and pre-
vented from workinpr. This is done by having a sufficient number
of widely spaced shrouds.
Types of Vessels. — It is scarcely necessary to remind any
reader that all vessels are not built for the same purposes, nor
92 KNOW TODB OWK SHIP
to eogstge in the same trades, or for tbe same claaa of harbours.
Naturally, therefore, one vessel cannot fulfil all requirements, and
be adapted for all traffio, and the result is a considerable variety
in the types of Teasels built. It is not uncommon to hear the
complaint lodged against a vessel that she is ill adapted for her
special trade, and the reason undoubtedly is, in many cases,
attributable to the fact that the wrong type has been selected to
comply with the necessary requirements, neither the shipbuilder
nor the naval architect with their wider experience, having been
consulted on the matter. Type, in the majority of cases.
BTR0CTUER. S3
depends entirely upon deadweight and internal capacity. The
heaviest cargoes, in comparison with their bulk, require the
least hold space. With the majority of cargoes it is quite
■ ■ i to design and fix upon a type of Teasel, so that, when
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l—J
-
-1
.
the holds are ^lled, she will float at het load water mark. But
it must also be obvious that there are some cargoes, such as
metal and ores, with which it would be impossible to fill the
hold apace, and not submerge the disc or eitreme load line at
the load water mark. However, for all purposes, theie ia a type
94 KNOW YOUR OWN SHIP.
of vessel most adapted for a particular kind of cargo. "With
light cargoes of small density which fill the holds and still leave
large freeboard, the shipowner does not mind so long as the
freights are satisfactory ; but naturally, when he gets cargoes of
greater density, which bring the vessel down to the waterline
obtained by the lighter cargo before her holds are filled, he
desires to decrease the freeboard, and to continue to decrease it
as the cargoes increase in density. Unfortunately, experience
has shown in some cases that this decrease would scarcely cease
until the freeboard had approached vanishing point; and thus,
for the sake of the safety of ships, cargoes, and lives, it has been
absolutely necessary to fix upon standard types of vessels adapted
to certain freeboards, which, as a rule, are most willingly
accepted by shipowners, and, indeed, in some cases, more free-
board is given to vessels by the owners themselves than even
the Board of Trade rules demand.
The heavier the cargo, especially in ships of great length to
depth, the greater the bending and twisting strains experienced
when among waves, and hence the greater necessity of increased
structural strength.
Vessels, according to their structural strength, etc., are classified
under different names or types, which are often heard and used,
but less often understood. There are, again, degrees in each
particular type ; for example, by 100 Al at Lloyd's is meant
vessels built to the highest class of their particular type, and
therefore fulfilling all the requirements for such class ; 95, 90,
and 80 A are lower classes, and do not therefore fulfil the require-
ments of the one above them. Such vessels have greater free-
board, and therefore carry less deadweight.
First. — The most important of these types is that known as
the Three Deck, This is the best deadweight carrier, and there-
fore ranks as the strongest type of vessel built. This is the type
of vessel used in illustrating the growth of structural strength
for size of vessel in figs. 45 to 51, and includes the smaller
vessels requiring only one or two decks.
Second, — A difficulty sometimes experienced in the three-deck
type was, that partly owing to the loss of cargo space occupied by
the shafting and enclosed by the tunnel, it was found impossible
with some cargoes to trim the vessel by the stern, as desired, and
hence, for part of the after length, the ship was increased about
4 feet in depth, and became known as the Raised QuaHer Decker
(see fig. 66). Such vessels are really parts of two different-
vessels joined together, and each built as near as possible to the:
previous rule for one-, two-, and three-deck vessels.
The sizes of all floors, frames, and reverses are governed byi
BTRUC^UBB,
95
Lloyd's first number to the main deck. The frames run up to
the quarter deck, and the alternate reverse frames also. The
number and arrangement of hold beams, beam stringei-s, and
stringers in hold in the way of the raised quarter deck, are in
accordance with the increased depth of the vessel at that part,
and the height of the reverse frames is regulated by the Lloyd's
first number, which the increased depth would give. The aim
•is to make the raised quarter deck an integral part of the whole,
and the result is that a great amount of extra strengthening has
to be introduced at the weakest part, which is in way of the
break, by overlapping the decks and stringers, doubling the
sheerstrake, and fitting webs between the overlapping part of
the two decks, 'So as to better bind the structure together (see
A, fig. 66). As the three-deck and the raised quarter-deck
vessels are types which secure least freeboard, it is usual and
1
Ti
1
BRiooe 0*
OIAPHRACM
\ PLATeS
i MAIN 0«
T
F
A
Fig. 66. — Raised Quarteii Decker.
I ^^b^koLb^
certainly of great value to erect a bridge over the engines and
boilers, and thus protect this most important part from the inroad
of the sea. In addition to this, for the accommodation of the
crew and passengers, a forecastle or poop is often erected, which,
according to their respective values of affording additional effective
buoyancy, may further be a means of reducing the freeboard
(see chapter on "Freeboard").
TJiird, — When a vessel is required to carry cargoes of lighter
density, it is usual to adopt the Spar-Deck type^ as these vessels,
while possessing the same interior cubical capacity as the three
deck, are of lighter construction, and have greater freeboard.
Fourth, — Where the 'tween decks is required for passengers,
or to carry very light cargoes of great bulk, the Awning-Deck
type is usually chosen, as the awning deck is simply a light,
entirely-closed superstructure over the main deck. Being of
lighter construction, she is less capable than either the three-
96 KNOW YOUR OWN SHIP.
decker or the spar-decker for carrying deadweight, and therefore
has the greatest freeboard.
Perhaps the simplest way of comparing the structure of these
types of vessels will be by referring to a midship section of each
of them.
Let figs. 67, 68, and 69 be midship sections of three vessels
identical in their exterior appearance, each being 260 feet long,
35 feet beam, and 24 feet depth to the uppermost deck at the
side from the top of the keel. Fig. 67 is the midship section of
the three-decked type.
Fig. 63 is the midship section of the spar-deck type, the spar
deck being the uppermost deck, and 7 feet above the main deck.
Fig. 69 is the midship section of the awning-deck type, the
awning deck also being the uppermost deck, and 7 feet above the
main deck.
We have already observed that Lloyd's first number governs
the sizes of all the frames, reverse frames, floors, bulkheads, and
pillars, and that the depth of one-, two-, and three-decked vessels
is taken to the uppermost deck. In the case of spar-and awn-
ing-decked vessels, the depth and girth are only taken to the
main deck, with the result that the first number for these
vessels is considerably reduced, hence the difference in the sizes
or scantlings of the frames, reverses, floors, bulkheads, and pillars
(compare respective sections). Then, with a reduced first number,
follows a reduced second number, governing the sizes of the
outside plating, keelsons, stringers, etc.
Thus far the spar- and awning-decked vessels are identical,
so we must note the distinction.
Spar-Decked vessels, according to Lloyd's, are supposed to have
three tiers of beams; and to be not less than 17 feet depth from
the top of the keel to the main deck. Should the depth be less
than this, a modification must be made in the freeboard assigned.
In all cases the frames extend from the keel to the gunwale ;
the reverse frames extend to the main and spar decks alter-
nately ; a thick sheerstrake is fitted to both the main and spar
decks; the side plating above the main-deck sheerstrake is less
in thickness than that below; the main and spar decks, when
of wood, are each Z^ inches thick, laid and caulked ; spar deck
beams, stringer and tie plates are lighter than those required for
the upper deck of three-decked vessels. Since the depth is only
taken to the main deck, and the strength above the main deck is
considerable, greatly increasing the efficiency of the ship girder
in resisting longitudinal strains, they do not require any addi-
tional strengthening for extreme proportions until over 13 depths
to length, while in the three-deck type over 11 depths to upper
STRUCTURE. 97
deck in length is considered an extreme proportion, thereby
requiring additional strengthening.
In Awning-Decked vessels all frames extend to the awning deck ;
the reverse frames extend to the main deck ; the side plating above
the main deck is greatly reduced, and no sheer-strake is fitted to
the awning-deck ; awning-deck beams are lighter than those
required for spar- decked vessels. Since the awning-deck is simply
a light superstructure, it is necessary that these vessels have a
complete main deck laid and caulked. These vessels are considered
of extreme proportions when over 1 1 depths to length, the depth
being taken to the main deck.
The reader will be greatly aided in grasping these differences
by comparing the sections.
Bulkheads. — Watertight bulkheads are iron or steel divisions
arranged either transversely or longitudinally, dividing the vessel
into watertight compartments. They also give strength, but their
chief function is to afford safety, so that, should any compartment
by any chance or accident be flooded, it is intended that the
vessel will still float in comparative safety. Most of the large
liners and warships built in these days are divided and sub-divided
into numerous watertight compartments, having bulkheads far in
excess of the requirements of Lloyd's, or any other classification
society. Thus it is possible in many cases for several of these
compartments to be damaged and flooded before endangering the
safety of the vessel.
Screw steamers classed at Lloyd's have a bulkhead at each end
of the engine and boiler space, and another near each end of the
vessel. The necessity of having the engines and boilers encased
in a watertight compartment is obvious. The foremost or col-
lision bulkhead should be situated at not less than about half the
midship beam of the vessel from the stem. The fore end of the
vessel being the part most likely to be damaged in case of colli-
sion, and the strain which comes from panting tending to make
leakage, explains the necessity of having this end of the vessel
watertight. At the after end of the vessel, however, though free to
some extent from the danger at the fore end, there is severe strain,
especially in high-speed vessels, due to the vibration of the shaft-
ing. As the danger is that the aft end shell plate rivets may be
worked loose and leakage occur, this part also is made watertight.
Though in short vessels it may be quite possible for one of these
five watertight compartments to be flooded, and the vessel to
remain afloat, it will be evident that in long vessels the lengths of
the fore- and after-holds would be so great that were one of them
damaged, and the sea to enter, the loss of buoyancy or floating
power would be so great that sinking would be inevitable.
G
98
KNOW YOUR OWN SHIP.
uo
Three- Deck Type— 10*4 depths to upper deck in length.
14-5 '.. middle
)»
»
Fig. 67. — Midship Section of a Thkke-Decked Type or Vessel,
STRUCTURE.
99
Lloyd's Numerals.
i Girth, .
I Breadth,
Depth, .
1st No., ,
Length, .
2nd No.,
39 1
17-5
24-78
81-33
7
74-33
258
19177
8 — 7
Frames, 5 x 3 x ~, spaced 24 inches.
20
Reverse frames, 3 x 3 x ^.
Floors, 23i X ^ ~ ^
20
Centre keelson, 22^ x
13 - 11
"20~"
Keelson continuous angles, 5^ x 4 x ^.
Intercostal keelson plate, ^.
Upper deck beams, 7i x^^, bulb plate with 1 ^ ^^ ^
Double angles, 3 x 3 x ^ j •'
Middle deck beams, SJ x ^^, bulb plate with \ ^nd frame
Double angles, 3 x 3 x A J ^ ^
Hold beams, QJ x ^ \ , q. , -
Double angles, 4 x 4 x ^ /^^ ^^^^^ ^^^^ *'^*°^®-
Upper deck stringer plate, 62 x ^ - 31 x ^.
Middle deck stringer plate, 52 x ^^ - 31 x ^.
Hold stringer plate, 34 x ^ - 26 x ^.
Gunwale angle bar, 4J x 4^ x 2®^.
Sheer strake, 42 x ^^ ~ ^^
Garboard strake, 36 x
20
12 - 11
20
Keel, 9^ x 2^.
Hold pillars, 3|.
Upper deck, 4 inches thick, laid and caulked.
Miadle deck, 3} inches thick, laid and caulked.
Additions for Extreme Length,
Centre keelson increased in depth.
To side keelson, a bulb is added for J L amidships.
To bilge keelson, a bulb is added for | L amidships.
To bilge stringer, an intercostal plate is added for J L amidships.
100
KNOW YOUR OWN SHIP.
. ^"'' 'TMII III limga;
rT
SMECR STRAKC
SMECII STRAKC
tta
20
tOS
Spar-Deck Type— 14§-2=12i depths in leiigtli.
Fig. 68.— Midship Section of a Spar-Dfxked Vessei,.
STRUCTURE. 101
Lloyd's Numerals.
i Girth, 32-1
I Breadth, 17*5
Depth 17*73
1st No., 67*33
Length, ....... 258
2nd No., 17371
7 — fi
Frames, 4 x 3 x , spaced 23 inches.
Reverse frames, 3 x 3 x ^V
Floors, 20i X ?-^.
20
Centre keelson, 17 x — ~ .
20
Keelson continuous angles, 5 x 4 x ^^y.
Intercostal keelson plate, ^7.
* Complete steel deck, ^,
Spar-deck beams, 7 x Z^, bulb plate with ) ^nd frame
Double angles, 3 x 3 x ^ j °" ®^®^y ^^^ ^^^^^'
8 — 7
Main deck beams, 6 x 3 x , bulb angle on every frame.
Hold beams, 9i x ^%, bulb plate with \ , q., .
Double angles, 4 x 4 x ^ /°^ ®^®^y ^^^^ "^*°^®*
Spar-deck stringer plate, 44 x .^ - 29 x ^^5.
Main deck stringer plate, 37 x ^^ - 29 x ^.
Hold stringer plate, 32 x ^\ - 25 x ^%.
Gunwale angle bar, 4 x 4 x -^jf,
Garboard strake, 36 x ^-^-1".
' 20
Keel, 9 x 2^.
Hold pillars, 3.
Spar-deck, 3^ inches thick, laid and caulked.
Additions for JExtreme Length,
To thickness of sheer strake, ^ is added for f L amidships.
To strake below sheer strake, ^ is added for J L amidships.
To bil^e keelson, a bulb plate is added for ^ L amidships.
To thickness of 2 strakes at bilge, -gV is added for ^ L amidships.
* Taking out the scantlings of this spar-decked vessel according to her numerals and
proportions, a steel deck is required, as shown upon the Midship Section. But Lloyd's
rules say : " In no case will the material at the upper part and the nim[iber and thick-
ness of steel or iron decks be required to be greater than that of the three-decked
vessel of the same dimensions." However, as a spar-deck vessel must have a complete
main deck laid and caulked, though it may be of wood 3^ inches in thickness, a common
practice among shipowners of choosing a steel deck has been followed in this Midship
Section.
102
KKOW YOUR OWN SHIP.
8-. -
* ■ SMCCR STRAKE
AND OOUSUNG
tu-9_
20
to d
20
20
STRAKE
OOUBLCD
AwniDg-Deck Type— 14*6 depths in length.
Fig. 69. — Midship Section of an Awning-Decked Vessel
STRUCTURE.
103
Lloyd's Numerals.
i Girth, 32-1
i Breadth, 17*5
Depth, 1773
IstNo., . . . . . . 67-33
Length, 258
2nd No., 17371
7 — 6
Frames, 4 x 3 x i — -— , spaced 23 inches.
Reverse frames, 3 x 3 x ■^.
Floors, 20i X ^-Zl.
* ^ 20
J*
Centre keelson, 17 x — ^~- ,
Keelson continuous angles, 5 x 4 x ^\.
Intercostal keelson plate, ^f^.
Complete steel deck, ^.
Awnmg-deck beams, 6| x 3 x ^%, bulb angle on alternate frames.
8 — 7
Main deck beams, 6 x 3 x — ^.- , bulb angle on every frame.
Hold beams, 9i x ^, with \ .q., .
Double angles, 4 x 4 x ^«^ /°'^ ®^®^ ^^^^ "*™®-
Awnin^-deck stringer plate, 32 x ^^.
Main deck stringer plate, 37 x ^^ - 29 x ^f^.
Hold stringer plate, 32 x ^p^ - 25 x ^f^.
Gunwale angle bar, 4 x 4 x ^^.
Garboard strake, 36 x 1L~J_^.
' 20
Keel, 9 X 2|.
Hold pillars, 3.
Awning-deck, 3 inches thick, laid and caulked.
Additions for Extreme Length,
Sheer strake, doubled whole width below stringer plate, for f L amidships.
To upper deck stringer, ^ is added for J L amidships.
One strake at bilge, doubled for ^ L amidships.
104
KNOW YOUR OWN SHIP.
Lloyd's, therefore, require that in vessels 280 feet and over in
length, an additional bulkhead be fitted in the main hold; and
when over 330 feet in length, another bulkhead be placed in the
after-hold.
All bulkheads should extend sufficiently high, so that in the
event of any compartment being flooded, there would not be the
danger of the water pouring over the top of any bulkhead. The
collision bulkhead should extend to the height of the uppermost
.INER
0)
u
z
u.
u
J
o
o
o
Elevatiou of bulkhead.
Ii.teraal view of ship, shcwiug'ccnnectioii of
bulkhead to shell.
BULKHEAD
SH^LL PLATING
B Plan
Fig, 70. — Connection of Bulkhead to Shell.
deck, and its watertightness tested by filling the foremost compart-
ment with water to the height of the load waterline.
The bulkhead bounding the engine and boiler space should
extend to the upper deck in one-, two-, and three-deck vessels; to
the spar-deck in spar-decked vessels ; to the main deck in awning-
decked vessels.
The aftermost bulkhead should extend to the upper deck, or to
the spar-deck, and should also be tested to ensure watertightness
by filling the after peak to the load waterline.
STRUCTURE. 105
Should the vessel be long enough to require other bulkheads,
they should extend to the upper deck in one-, two-, and three-deck
vessels ; to the spar-deck in spar>decked vessels ; and to the main
deck in awning-decked vessels.
The bulkhead plating is attached to the shell of the vessel by
double frames (fig. 70).
It often occurs that it is not convenient to carry a bulkhead
continuously from the keel to its required height, but it is
recessed or stepped in the form of a plated flat at an intermediate
part, and then continued to its prescribed height. (See A, fig.
71.) However, the watertightness must be maintained. This
may be done by cutting the reverse frames and fitting angle
collars round the frames in way of the flat, as shown by B, in fig.
71, or cast-iron chocks between the frames (C, in fig. 71), or else
the frames may be cut, and the flat connected to the shell by a
continuous angle, with brackets above and below joining the flat
to the frames (D, in fig. 71). When a bulkhead is stepped on a
water ballast tank it should be connected by double angles, or in
the case where it terminates at a deck, or is fitted in a 'tween
decks, it should be attached to the decks by double angles.
Where a bulkhead extends above an iron deck, the longitudinal
strength is preserved by keeping the deck continuous, and stopping
the bulkhead at the under side, then continuing it again above
the deck, making the connection by double angles. In fitting
iron collars in w^ay of a watertight flat, the reverse frame is cut
and the main frame doubled for about three feet to compensate
for the break in the reverse frame. Being very expensive, this
method is not often adopted. When cast-metal choeks are fitted
they are first bedded in cement, and a space of about three-
quarters of an inch left all round. This space is filled with metal
filings — the waste from drilling machines — which, when rusted
and caulked, forms very satisfactory watertight work. The edges
and butt laps in all bulkheads must be caulked. This is necessary
on one side only. It is better to caulk the collision bulkhead on
the after side, and the aftermost bulkhead on the fore side. One
reason for this is that it is more easily done ; but the chief one is,
that when these peaks are tested by a head of water, should leak-
age take place, the exact spot is easily perceived and caulked.
For the other bulkheads, it is of little consequence on which side
they are caulked.
It is always better to avoid any abruptness in longitudinal
strength, and thus all keelsons and stringers should be continuous
through bulkheads. This necessitates making the bulkheads
watertight at these places by fitting angle collars on one side of
the bulkhead, and often plate collars on the other. The angle
106
KNOW YOUR OWN Sfil^.
V
FLAT
CNLARCCO View OF ONC FRAMCSPACC AT C
SECTION
THROUGH
c
WATERTIGHT
FLAT
P=\lr-iJj-i1'
Fig. 71. — Recessed Bulkhead and Watertight Flat.
STRUCTURE.
107
collar is fitted on the side on which the bulkhead is caulked, and
is itself caulked (see fig. 72).
As has already been pointed out, if any part of the vessel is
subject to any weakening, compensation must be made in some
form or other to recover the strength. It will be noticed that in
attaching bulkheads to the shell plating, a double row^ of holes has
to be pimched, one of which is spaced 4 to 4J diameters apart.
The result is that the shell plating round the whole girth of the
vessel has been greatly weakened. Compensa-
tion is made for this by fitting what are called
liners in the way of all outside strakes, where
practicable. These are plates extending, as
shown in A, fig. 70, for at least two frame
spaces from the toe of one frame to the heel
of another, and from the edges of the two
inside strakes adjacent. The riveting in
bulkhead liners is arranged where convenient.
Longitudinal bulkheads continuous all fore
and aft in twin-screw vessels also provide a
means of subdivision, but at the same time they
may afford great longitudinal strength if well
constructed and stiffened, especially in very
long vessels, and more particularly so in long,
shadow vessels of the light draught type.
Their value in stiffening ships has been proved in cases where,
before they were fitted, the vessels suffered greatly from vibration
from the machinery, but after they were fitted the vibration was
greatly reduced. The reason of this is explained by our girder
illustration. The ship, being a hollow^ girder, has its upper and
lower flanges (decks and bottom) the more effectively united, and
by this means the whole structure acts more in unison in resisting
either local or general strain.
All bulkheads must be thoroughly stiffened if they are to be of
any service. To simply fit the sheet of comparatively thin plating
of which bulkheads are made, from side to side of the vessel, would
be useless in resisting any severe pressure. Bulkhead stiffening
is composed of angle bars of the size of the main frames of the
vessel placed vertically on one side, 30 inches apart, and on the
other side, horizontally, 48 inches apart. According to the
dimensions of the bulkhead, additional stiffening may be fitted in
the form of semi-box beams, web plates, and bulb angles. In all
cases the collision bulkhead should be additionally stiffened, since
this is most liable to danger.
Elspecially in the case of passenger vessels and yachts, it is often
found necessary to have a means of passage through a watertight
Fig. 72. — Angle
Collars mak-
ing Bulkhead
Waterti ght
ROUND Keel-
son.
108
KNOW Your own ship.
bulkhead, in order to get from one part of the accommodation
to another. This is done by fitting iron doors, which can be
closed and secured so as to make the bulkhead perfectly water-
(TTTrTTT)
^ — -fz —
r
n
i?.^j
®
(7TTTTTT)
;t.'4>
(TTT?T7T)
=^
.V
S
SECTION
WKOCK
PLAN
INDIA -RUBBtK
STEEL WEDGE
STEEL WEDCe
s
INDIA- RUDDER
Eulai'ged sketches showing two different methods of making doors watertight.
Fic. 73. — Bulkhead Watertight Door.
tight (fig. 73). When such a door is absolutely necessary, it
must be provided, but whenever possible it should be dispensed
with, for in case of accident it is very often found that the
numerous watertight compartments into which the vessel has
STRUCTURE.
109
o o
o o
o o
o o
o o
o o
^
BUTT STRAP
Fig. 74. — Butt Strap.
probably been divided in order to secure safety under the most
exceptional circumstances, are rendered worthless, and sometimes
a source of danger by these doors being left open, and either
forgotten or unapproachable in the hour of need.
Riveting. — A most important consideration in the production
of an efficient vessel is good workmanship, and the greatest
attention should be paid to sound riveting and accurate fitting of
butt straps, etc. (fig. 74). Blind or unfair holes are often the
result of carelessness on
the part of workmen in
marking off the spacing,
or in punching the rivet
holes. Where such occur,
however, the drift punch
should be strictly for-
bidden, as its use not only
tears and weakens the plate
by the severity of its action,
but to get thoroughly
watertight work is rendered most difficult, as the rivet cannot
fill up the cavities made in so damaging the plate. The drift
punch is a tool, as shown in fig. 75, circular in section, which is
driven into the hole, and a space
for the rivet torn through.
The proper method, when such
holes do occur, is to rime them with
a tool (fig. 75), which cuts away
any projecting material and leaves
a clean hole for the rivet.
After a rivet has cooled down,
and is found to be slack, or that
the head has been badly laid up,
or that, on testing, leakage takes
place, the rivet or rivets should
not be caulked to ensure water-
tightness, as is sometimes done, but taken out and re-riveted.
Were it not for the additional cost, it would be better to rime
out punched holes before riveting, as this would not only clear
the rivet holes, but to some extent restore the strength of the
plate, which is weakened by the severity of the action of punching.
Though much more costly, by far better work is obtained by
drilling rivet holes, as this process not only gives fairer holes, but
does not by its action weaken the plate.
In punching rivet holes in plates or angle bars, the holes are
always punched from the faying surfaces — that is, from the sur-
o
DRIFT
PUNCH
m
w
RIMER
Fig. 75.— Drift Punch
AND Rimer.
110
KNOW YOUR OWN SHIP.
faces which are to lie against each other. By this means the
plates fit hard up to each other, as a rag edge is made on the
Outer surface of the plate in punching.
Thus in the plates in A, fig. 76, the holes are punched in the
direction shown by the arrows. In machine punching, the rivet
holes gradually increase in diameter in the direction in which the
punch passes, as shown.
A few forms of riveting may here be taken with advantage.
For watertight work, where one surface of the plating has to be
flush, the pan head rivet is undoubtedly one of the best. Its form
is as shown in B, fig. 7fi.
It will be observed that the neck of the rivet is expanded under
L
I
X
C D E
Fio. 76.— Mode of punching Rivet Holes, and Forms of Rivets.
the pan head ; this, when heated and hammered, completely fills
up the hole in plate a. In plate h^ after the rivet hole has been
punched, it is drilled by a machine into a more conical form, as
shown. This is called countersinking. When the rivet head is
thoroughly beaten up, it is cut off in a rounded form, leaving it
rather full on the flush surface of the plate. In cooling, the rivet
contracts, and this further tends to effectually close up the hole.
Another form of rivet is shown in C, fig. 76. The further this
rivet is driven into the hole the tighter it wedges itself, and, if
well hammered and laid up, it produces good results. It is still
further improved if the work is not prominently visible, by laying
up a point as shown in D, fig. 76, producing greater holding
power. This also applies to the pan head rivet, which, as has
been proved by experience and experiment, is then the most
efficient rivet.
8TBUCTURB. Ill
For the sake of their better appearance, the snap head form of
rivet has been considerably adopted in many parts of the structure
exposed to view, especially in bulkheads. But hand-riveted snap
head rivets have not produced satisfactory results. In clenching
up the point of the rivet with the tool called the snap cup^ the
effect is to bring the edges of the rivet close, in the form of a point,
as shown in E, fig. 76, leaving a hollow all round under the head
of the rivet.
So long as the rivet is kept dry it works weU enough, but when
water gets to it the pointed edge rusts, and corrosion is set up in
the plate also, with the result that, after a time, the rivet works
loose, and, in many cases, they can be twisted round by the fingers.
Where the work has to be strictly watertight, a far better result
is secured by simply hammering the point down hard on the plate,
though the appearance is certainly not so taking. Nevertheless,
appearance should be sacrificed, rather than efiiciency and
strength.
Where snap riveting is performed by a machine, however, the
results are very satisfactory, since the machine has the power of
more effectually clenching up the point of the rivet. But it is
only in some parts of the structure where machine riveting can
be carried out, although in every case it is superior to hand
riveting.
112 KNOW YOUR OWN SHIP.
CHAPTER VI. (Section I.)
STABILITY.
Contents. — Definition — The Righting Lever — The Metacentre — Righting
Moment of Stability — Conditions of Equilibrium — ** Stiff" and
"Tender" — Metacentric Stability — Moment of Inertia — Agents in
Design influencing Metacentric Height — How to obtain Stiffness —
Changes in Metacentric Height during the Operation of Loading —
Stability of Objects of Cylindrical Form — A Curve of Stability —
Metacentre Curves — How the Ship's Officer can determine the Meta-
centric Height and then the position of the Centre of Gravity in any
condition of Loading — Effect of Beam, Freeboard, Height of Centre
of Gravity above top of Keel, and Metacentric Height, upon Stability
— "Wedges of Immersion and Emersion — Effect of Tumble Home upon
Stability — Stability in Different Types of Vessels.
Definition. — By the term stability la meant the moment of
force (usually measured in foot-tons, or in inch-tons), by means
of which a vessel, when inclined out of the upright position
through some external force, immediately endeavours to right
herself. Stability is dependent upon design and loading.
Many ocean-going craft have not sufficient stability to stand
upright when light, and loll over, and some will not stand at
all in this condition without ballast. But ships are not built to
sail upon the open sea light, and these same vessels may be so
regulated in the operation of loading as to be changed into
splendid sea boats.
The Righting Lever. — In Chapter II. we explained the
meaning of a foot-ton — viz., that 1 ton of force multiplied by a
leverage of 1 foot equals 1 foot-ton. Now, if we say that a
vessel of 1000 tons displacement has a righting moment of
stability of 2000 foot-tons when inclined to an angle of, say, 30',
we mean that the weight, 1000 tons, is acting at a leverage of
2 feet, since 1000 x 2 = 2000 foot-tons ; and this is the
righting tendency possessed by this ship when inclined to an
angle of 30**. The two factors in the moment of stability are
weight and leverage. The weight is always the total displace-
ment.
The leverage we shall now endeavour to explain.
StABliilTY.
113
Fig. 77 represents two midship sections of the same vessel, one
floating upright and the other inclined to an angle of about 14**.
When she floated in the upright condition, W L was the water-
line ; the point B is, at the same time, the centre of buoyancy or
centre of gravity of the water displaced by the ship, and G is, for
that -kind of loading, the centre of gravity of the ship and her
loading. But when the vessel became inclined, as in the sketch,
she floated at the waterline W L'. Observe what has happened.
The displacement has certainly changed in form, but not in total
volume or weight ; that remains exactly the same, because the
weight of the ship and the cargo remain exactly the same. But
the centre of buoyancy has moved towards the right to B', which
is the new centre of displacement (that is to say, the new centre
of the water displaced by the heeled ship), the old B being no
-^
Fig. 77. — Vessel floating Upbight, and Inclined 14''.
longer that centre. The centre of gravity of the ship and its
loading, G, remains in the same position in the ship as before,
whatever be the angle of heel, so long as we do not alter the
loading. It must always be the centre of weight, and will never
move, as just stated, so long as the weights on board remain
stationary. The weight of the ship, like all weights, acts
vertically downward through its centre of gravity, G, and the
pressures of buoyancy act vertically upward through the centre
of buoyancy, B or B', as the case may be. When the ship was
upright, the two points were in the same vertical line, but after
being inclined, their forces acted through their centres in the
direction of the arrows on tKeir vertical lines of action, leaving
a horizontal distance between them, because, now they are not in
the same vertical line. This perpendicular — that is to say,
horizontal — distance between the two vertical lines of action,
gives the lever, GZ; and this very important distance, GZ, is
114 KNOW YOUR OWN SHIP.
the lever we want, and which we mentioned previously as one
of the factors in the measure of a vessel's stability.
The Metacentre. — It will be noticed that the vertical line
through the centre of buoyancy intersects the centre line of the
section of the vessel at the point M. This point is called the
metacentre^ and is always at the intersection of these two lines,
which is approximately a fixed point up to angles of about 12**
or 15** of heel for ship-shaped objects. Usually, at greater
angles, the vertical line through the new B' no longer intersects
the centre line of the ship at the point M.
Righting Moment of Stsi-bility. — When M is above G, the
lever is properly termed a righting leveVy for then the action of the
buoyancy is to push the vessel again into the upright position, as
can easily be seen in fig. 77. When M is below G, the tendency
is to add to the inclining force, and in this case the lever is an up-
setting one. In the sketch, it is evident that the lever is a
righting one, and therefore the displacement of the vessel multi-
plied by this leverage measured in feet, say, at any particular
angle of heel, gives the righting moment of stability in foot-tons
for that angle.
Conditions of Equilibrium. — So long as there is a leverage,
the vessel, if left free to move, will not remain at rest, or, as it is
generally termed, in a state of equilibrium ; and the longer the
leverage, the greater is the moment tending to bring her back to
the upright condition, or to capsize her, as the case may be ; and
the longer the righting lever up to angles of 12° or 15° in
ordinary vessels, the higher must the metacentre be above the
centre of gravity. Thus, for a vessel to float upright in a state
of equilibrium or rest, it is evident that the centre of buoyancy
and the centre of gravity must be in the same vertical line, the
force of gravity of the ship and buoyancy of the water neutral-
ising each other. But it dues not follow that in this condition
the equilibrium will be stable. For if, under the effect of some
external force (such as wind), the vessel heel, and the metacentre,
before heeling, be below the centre of gravity, the result will be
to push the vessel further over, not necessarily by any means to
capsize her, but (it may be) to a position such as to cause the
upward vertical line of action of the buoyancy to coincide with
the downward line of action of the weighty when the vessel will
again remain at rest. When the vessel floated upright before
the inclination took place, she might have been compared to a
child's play top carefully balanced upon the point, a condition
it would not be likely to remain in for a long period. This
equilibrium is called unstable equilibrium. When the meta-
centre is above the centre of gravity, and thus, under the least
•
STABILITY. 115
inclination, the vessel immediately endeavours to regain the
upright condition, the equilibrium is termed stable equilibrium.
"Stiff" and "Tender." — When the metacentre is high
(equivalent to large righting leverage), and the righting moment,
when the vessel is inclined, is therefore great, the vessel is said
to be " stiff,^^ and when the metacentre is closer to the centre of
gravity, and the vessel naturally possesses small righting leverage
for small angles of inclination, she is said to be "craw/<;," or, as
sailors more commonly say, "^e/icZer."
When the centre of gravity and the metacentre coincide — that
is, when both j)oints occupy the same position, — the equilibrium
is then neutral, neither stable nor unstable.
Metacentric Stability. — Having foimd the distance between
the metacentre and the centre of gravity, the actual lever of
stability may be found for small angles of heel not exceeding
15', by multiplying this distance by the sine of the angle of
heel (using natural sines*).. Then leverage in feet multiplied
by displacement in tons equals righting moment in foot-tons.
This stability, which is deduced from the metacentric lieiglif,
or, distance from M to G in fig. 77, is termed metacentric
stability.
Our next endeavour must be to discover the position of these
points, and to ascertain how they are influenced. The centre of
buoyancy we have already studied in Chapter III., and have
found its position to be always in the centre of displacement,
and also, when the vessel is floating upright, that it is always
a fixed point at any particular waterline.
The metacentre also is a fixed point for each successive draught
when the vessel floats upright, and thus, by calculating a few of
these points, a curve may be constructed, thereby enabling the
position of the metacentre to be ascertained at any draught.
But, first of all, let us see how the design or dimensions of a
vessel affect the position of the metacentre. The formula for
finding the metacentre is : —
Moment of inertia of waterplane _ / Height of metacentre above centre of
Displacement in cubic feet I buoyancy.
To give the usual definition of Moment of Ineiiia would prob-
ably be to sound the keynote of despair to many a seaman.
A simple, though perhaps not very scientific method may be
used, reducing this to terms sufficiently plain to be understood
by seamen with the most limited mathematical knowledge.
* See table of natural sines at end of book. Such a table is printed in
many books on Navigation,
116 KNOW YOUR OWN SHIP.
Moment of inertia may be understood as the measure of the
tendency possessed by the superficial area of the waterplane of
any floating object, to remain inert, dead still, or motionless. It
must be clearly understood that this moment of inertia applies
only to the waterplane area at which the vessel is floating, whether
the vessel be a ship, a box, or a log of wood. Thus, the fact that
there may be one part of the floating object out of the water, and
another part in it, is left entirely out of consideration. Simply
area at the waterline is dealt with. The formula for moment of
inertia of a rectangular-shaped waterplane is as follows : —
Cube the side at right angles to the longitudinal axis, multiply
this by tJie length of tJie waterline, and divide the result by 12.
Note, — All measurements should be in feet to match the displacement.
-y-
LoMCiTUDiNAu Axis
1
^ 50 >^
\ 1
Li--
Fig. 78.— Plan of Waterplane.
For example, take ^g, 78, which is a plan of the waterplane of
a box-shaped vessel 50 feet long, 10 feet broad, and 8 feet draught.
The moment of inertia would be : —
102_x^ = 10 X 10 X 10 X 50 ^ 4igg.gg ^^^3^^ ^f .^^^^.^
12 12
The student should note that since the dimensions and area
of all the waterplanes of a box-shaped vessel, floating with the
bottom parallel to the waterline, are equal to one another, the
moment of inertia of each waterplane is the same.
But let us proceed to find the height of the metacentre. This
is done by dividing 4166*66 by the displacement in cubic feet;
the result is the height of the metacentre above the centre of
buoyancy. The draught is 8 feet. It is, therefore, evident that
the object, being of box form, the centre of buoyancy must be at
half the draught, which is 4 feet above the bottom. The dis-
placement in cubic feet will be the volume of the part of the
vessel immersed, which equals : —
50 feet length x 10 feet breadth x 8 feet draught = 4000 cubic feet
displacement.
Then ~ " . = i '04 feet height of metacentre above centre of buoyancvr
4000 ^
STABILITY. 117
Now, the question may be well asked at this stage — Of what
value is this result? The only answer is, that these points, by
themselves, are of no practical use, and give no idea whatever of
a vessel's stability, until we get the position of the centre of
gravity. Let us suppose the height of the centre of gravity from
the bottom of the box to be 3 feet (the box having, of course, a
load in its lower part, so as to keep the centre of gravity of the
loaded box down to 3 feet).
Since the metacentre is 1*04 + 4 = 5*04 feet from the bottom
of the box, therefore the distance of the centre of gravity below
the metacentre is 5*04 - 3 = 2*04 feet, proving that the vessel
is floating in a condition of stable equilibrium. While floating
at this • draught, imagine a weight of 20 tons already on board
to be raised 13 feet. Observe distinctly the new state of afiairs,
supposing that after the alteration the vessel floats upright.
The displacement, the positions of the centre of buoyancy and
metacentre are all just the same as previously, no alteration
having occurred in the draught. There has, however, been a
change in the position of the centre of gravity, thereby affecting
the distance between the changed centre of gravity and the
unchanged metacentre. Any vertical movement of weight in
the box must either raise or lower the centre of gravity, con-
sequently, in the case before us, since the weight of 20 tons was
raised, it follows that the centre of gravity must have travelled
in the direction of the shifted weight. But how far? We
have already discovered how to find this in the chapter on
" Moments," viz. : —
Multiply the weight by the distance it has been maved, and divide
hj tlie total displacement (4000 cubic feet = 114*2 tons),
20 X 13 ^ o .o feet = i Distance centre of gravity
114-2 t has moved upwards.
We now see that the centre of gravity, instead of being below
the metacentre as previously, has risen to (2*2 - 2*04) = 0*16 of
a foot above it. If the box remain upright, it is in a condition of
unstable equilibrium, and any exterior force upon it will readily
cause it to heel. As the vessel has not sufficient stability to
float upright, the vital question is — Will she capsize? In the
example before us, the vessel having a good freeboard of about
5 feet, the answer is "no," for, after inclining to an angle of
about 18", she would remain at rest with this permanent list.
Let us again investigate the circumstances. The centre of
gravity has remained stationary imder the inclination. We
observe a slight movement of the centre of buoyancy from its
118 KNOW YOUR OWN SHIP.
old position to the new centre of displacement. In the earlier
stage of this inclining movement, the vertical line through the
centre of buoyancy intersected the centre line of the vessel below
the centre of gravity, in fact, as always for very small heels, at the
metacentre, making a leverage between the vertical lines through
the centre of buoyancy and the centre of gravity. This point
of intersection being below the centre of gravity, the heeling
continues, for the moment is an upsetting one, the buoyancy
expending itself in pushing the vessel further over. Reference to
Hgs. 16 and 77 will assist in tracing the movements of these points.
However, after inclining to an angle of about 18°, it would be
found that the centre of buoyancy had travelled so far out
towards the inclining side as to bring it vertically beneath the
centre of gravity, the vertical lines of action through these two
points coinciding. The upsetting lever having vanished, the
box floats in a condition of equilibrium, having neither righting
nor capsizing moment, and will move neither towards the port
nor the starboard except by the application of sheer exterior
force. For vessels of cylindrical form, and, therefore, circular
in section, the metacentre is the point of intersection of the
vertical line through the centre of buoyancy with the centre
line of the cylinder /or oM angles of inclination, and, knowing this,
we shall soon see how the whole range of such an object's stability
may be readily determined. As we have observed, vessels of
ship form differ from cylinders for large angles of inclination, and
another method has to be adopted in order to trace out the
whole range of stability. See Stability Calculation, Chap. X.
Agents in Design Influencing Metacentric Height. — The
two important factors in the design of a ship influencing the
height of the metacentre are beam and displacement. The
formula for the moment of inertia of the waterplane of a box
vessel we have already stated as: —
Length x Breadth^
12 '
so that, as the breadth is cubed, any addition to this dimension
must have greater eflect in increasing the moment of inertia of
any waterplane than a similar addition to the length.
The formula for height of metacentre above centre of buoyancy
is : —
Moment of inertia of load waterplane
Displacement
It must, therefore, be evident that the smaller the displace-
ment, the greater will be this height. Had the displacement of
STABILITY., 119
the box vessel, referred to previously, been reduced by cutting
ojffthe bottom corners and making it more triangular in shape,
preserving the same area of waterplane, a much higher metacentre
would have been obtained. Thus, fine vessels with good beam
produce the highest metacentres. These points may be more
vividly illustrated by means of a few simple examples : —
Let 2 feet be added to the beam of the box vessel with which we have just
been dealing, the draught remaining the same. The dimensions will now be
— Length, 50 feet ; breadth, 12 feet ; draught, 8 feet.
The moment of inertia = ^^ "^ ^^ - 7200.
12
The displacement =» 50 x 12 x 8 =- 4800 cubic feet,
7200
4800
1 '5 feet = metacentre above centre of buoyancy.
In the original condition, the metacentre was 1*04 feet above the centre of
buoyancy, and 2*04 feet above the centre of gravity.
The metacentre, being raised (1*6 - 1*04 ==) 0*46 of a foot, by the addition
of 2 feet to the beam, in its turn increases the metacentric height to
(2*04 + 0*46 =) 2*5 feet, greatly adding to the stiffness of the vessel.
Had we added 2 feet to the length of the vessel, certainly the moment of
inertia would have been increased, but so would the displacement, entirely
neutralising what might have been imagined a means of raising the meta-
centre.
52 X 103 ^ ^ggg.gg ^0^3^!. of mcrtia.
12
52 X 10 X 8 = 4160 cubic feet displacement,
4333*33
. ;— = 1*04 feet metacentre above centre of buoyancy, and
4160 ^ ^
the same as the original height.
If 2 feet had been added to the draught, the moment of inertia would
have remained the same: — ^ — — = 4166*66, and the displacement would
naturally have been enlarged, 60 x 10 x 10 = 5000 cubic feet. The evident
result must be that in relation to the centre of buoyancy, the metacentre is
now lowered, for ^--^^- = 83 of a foot metacentre above centre of buoyancy,
5000
which is less than the original 1 *04.
By these simple illustrations it is clear thai team is the most
important factor in the dimensions of a vessel by means of which
a high metacentre is obtained, simply because the breadth of the
vessel is used in the third power, while the other dimensions are
used only in the first power, in the process of calculation. It
will also be noticed that the position of the weights carried
120 KNOW YOUR OWN SHIP.
governs the position of the centre of gravity of the loaded
vessel.
How to Obtain StifEhess. — We have now discovered two
means of obtaining stiffness — first, by placing heavy weights as
low as possible, thus drawing the centre of gravity down from
the metacentre ; and second, by adding to the beam to raise the
metacentre.
Changes in Metacentric Height when Loading. — We can
also the better understand how it is that some vessels, especially
when loaded with homogeneous cargoes, get tender when the
last part of the cargo is being put on board, and the load water-
line approached. For some distance below the load waterline,
little or no increase has occurred in the area of the waterplane.
In fact, where the vessel possesses great tumble homey* it may
even happen that the width of the waterplane at ihe load line is
less than at 1 or 2 feet below it, and we have seen what effect
any reduction in the beam has upon the moment of inertia.
Now, while with increasing load, no increase may have been
occurring in the moment of inertia while nearing the load water-
line, the displacement has certainly continued to increase with
the increasing load. The metacentre and the centre of buoyancy
have, therefore, come nearer each other. But at the same time,
the centre of buoyancy has certainly risen above the keel some
distance, being now the centre of a greater displacement, and
may have risen more than the metacentre has sunk. The result
is that the metacentre may actually be higher from the keel
than before. But the continuation of the loading producing this
rise in the centre of buoyancy above the keel has also raised the
centre of gravity above the keel, with the eff'ect of reducing the
distance between the metacentre and the centre of gravity —
that is to say, the metacentric height is reduced, or, the vessel
has become more tender. Before any cargo was placed on board,
the metacentre and the centre of gravity had perhaps only 5 or 6
inches between them. In this position, the vessel would be tender,
not at all uncommon when light. Now, let the centre of gravity
of the unloaded ship be at half the depth of the hold. It is clear
that when the operation of loading commences, and as long as
weight is being placed below the centre of gravity, the centre of
gravity must be gradually lowering, and the vessel becomes very
stiff in consequence, but as cargo continues to be loaded, and the
holds are about filled, the centre of gravity rises again. It is
also evident, that if more heavy cargo be placed above the original
* "Tumble home " is the difference between the amidship breadth at the
uppermost deck edge and the moulded breadth.
STABILITY.
121
centre of gravity than below it, the centre of gravity must be
higher than it was previously. We must not forget, however,
that the metacentre has varied with every change of draught. If
we had a curve of metacentres for the vessel, we could readily
ascertain its correct position. If it were found that we had so
loaded our vessel as to bring the centre of gravity again into
proximity to the metacentre, the result would naturally be a small
metacentric height and a tender ship.
Stability of Cylindrical Objects. — At this stage, it will
repay us to give a little attention to the stability of objects of
cylindrical or cigar form, and from these simple shapes to deduce
such principles as will help us in dealing with the more com-
plicated ship forms.
Let fig. 79 be such an object 50 feet long, 10 feet diameter,
and for the sake of example, a solid piece of timber, floating half
Figs. 79, 80, 81.— Stability of Floating Cylindrical Objects.
immersed — that is, at 5 feet draught. The centre of gravity will
be in the centre of the log at G. Every reader knows from
observation that such an object will float as readily in one position
as another, and with any of the points, a, 6, c, d^ uppermost.
Such a condition is, therefore, one of neutral equilibrium, and this
being the case the metacentre and the centre of gravity must
coincide. Let us endeavour to prove this. It is clear that G is
the centre of weight. The centre of buoyancy will be in the
centre of the half circle in the water at B. If a piece of cardboard
were cut to this shape, and balanced upon a point, it would be
found to be '4244 of the half diameter of the cylinder down from
the line CD = -4244 of 5 feet = 2*122 feet. The moment of
inertia of the waterplaae will be
50 X IQS
= 4166-66,
122
KNOW YOUR OWN SHTP.
The displacement is
102 X -7854 X 50
= 1963-5.
A 1 dd'C fi
Therefore, ^ — = 2*122 metacentre above centre of buoyancy,
bringing it exactly up to G, thus proving the fact that the vessel
floats in a condition of neutral equilibrium.
Had the above cylinder been made of heavier wood, so as to
float deeper, as shown in fig. 80, its equilibrium would still have
been neutral, and in like manner the metacentre and centre of
gravity would have coincided.
Or again, had the object been made of lighter material, and
floated as in fig. 81, the equilibrium would have been unchanged,
for still the metacentre and centre of gravity would have occupied
the one position.
The fact to be remembered from these examples is, that tJie
transverse metace7itre is always the centre of the circular section
whatever he the draught.
w
w;
t
1
1 >
/
Fig. 82. — Vessel loaded with a Fixed Weight.
But suppose the vessel is hollow, and a weight is placed inside
and firmly fixed, with the effect of lowering the centre of gravity,
say, 1 foot below the metacentre. The vessel floats, say, at
half the diameter draught, 5 feet. To whatever angle the
vessel be now heeled, the centre of buoyancy must always be in
the centre of the immersed semicircle, and the centre of gravity
is immovable in its position.
When floating upright, as shown in fig. 82, the metacentre,
centre of gravity, and centre of buoyancy are in the same vertical
line ; but if the vessel be heeled, the centre of gravity and centre
of buoyancy will no longer be in the same vertical line. The
distance between the two vertical lines through the points (t
and B' indicates the lever of stability, GZ.
STABILITY. 123
In heeling, it is clear that a part of the vessel of wedge shape,
L M Z (fig. 83), formerly out of the water, is now immersed, and
another wedge-shaped part, WKw, formerly in the water, has
become emerged. Whenever it happens, whatever be the type of
floating object, that the immersed wedge
is identical in shape with the emerged
wedge, with each of their centres the
same distance from the vertical line
through the centre of buoyancy, this
vertical line will intersect at the point M,
in the line a 6, thus keeping the distance
from M to G (the metacentric height)
the same.
The lever of stability can be found
by multiplying the distance, MG, by the
sine of tJie particular angle of heel. This
is true for all floating objects of cylindri- ^^^' ^^•
cal form; and thus it matters not how
great may be the angle of heel, it is always found that the
immersed wedge, L M Z, is equal both in shape and volume to
W M «?, and also that their centres, P and K (see figure), are at
equal distances, x, from the vertical line through B'. Knowing
this, we can proceed to ascertain the whole range* of stability for
our cylindrical vessel. The calculations for the levers of stability
will be made at every 10° of heel.
A very simple method of illustrating the levers of stability for
cylindrical vessels (and one which the reader might well try for
himself, thereby proving by measurement the accuracy of the
calculation) is as follows : — Cut a piece of cardboard circular in
shape, and mark upon it in black dots the positions of the meta-
centre, the centre of buoyancy, and the centre of gravity (1 foot
below the metacentre) in the upright condition. Loosely attach
the cardboard to a flat board, placed vertically by means of a
screw through the point indicating the metacentre, so as to be
free to revolve. Over the head of the screw loop a thin length of
cord, and to the other end attach a button or round piece of lead,
so as to exactly cover the centre of buoyancy. Knot another
piece of cord, and pass it through the back of the cardboard at
the point indicating the centre of gravity, and at an indefinite
length hang another button or weight. When upright, the two
cords will hang together, but immediately the cardboard diagram
is inclined the cords will separate, and the perpendicular distance
between them represents the lever of stability. By revolving
* By range is meant the extent of the inclination from the upright
position to the angle at which a ship's righting force vanishes.
124
KNOW YOUR OWN SHIP.
the diagram at intervals it will be found that the levers measure
-| 1 T I I
0.334
pa
<
ft*
O
>
Pi
o
00
O
according to the calculation G M x sine of angle of heel = lever
of stability. [Nofe.—G M = 1 foot.]
STABILITY. 125
Lever at 10° = 1 x sine of angle of 10" -1736 = -17
20° = 1 X „ 20° -3420 = '34
>i
30° = 1 X ,, 30° -5000 = -50
j>
40° = 1 X ,, 40° -6427 ^ 64
) )
i)
0° = 1 X ,, 50° -7660 = -76
))
60" = 1 X „ 60° -8660 = '86
>>
70° = 1 X ,, 70° -9396 = -93
} >
80" = 1 X ,, 80° -9848 = '98
> J
90° = 1 X ,, 90° 1-000 = 1
To Construct the Curve of Stability (see fig. 84). — Draw
the horizontal line A B, and upon it at regular intervals mark off
spaces, each indicating 10** of heel. The 10** spaces may be
further subdivided into tenths, each representing 1° interval.
From the point A draw the vertical line A C, and upon this line
construct a scale of levers of stability, each space representing '1
of a foot. Using the scale AG set up at the 10°, 20**, 30°, etc.,
intervals, their corresponding leverages, '17, '34, '50, etc., and
through all these points run a curve. By means of this curve,
leverage at any intermediate angle of heel can now be readily
measured. In the figure before us, we see by the diagram that
the righting lever of stability steadily increases up to 90°, where
Fio. 85.— Wedges of Immersion and Emersion practically equal
Sectors of the same Circle for Small Angles of Inclination.
it attains its maximum length ; after that it gradually decreases,
exactly opposite to the way in which it increased, until at 180° it
vanishes altogether. The lever then begins to grow again, no
longer a righting one, but an upsetting one, and it continues to
increase up to 270°, where it is longest. After that, it again
diminishes, until, when a whole revolution has been made at
360°, the vessel once more becomes stable.
But the question may be asked — How comes it that for vessels
of ship form the vertical line through the centre of buoyancy only
intersects the centre line of the ship at the metacentre for small
angles of heel up to 12° or 15°, and at larger heels usually does
not ? The reason is simply this : —
126 KNOW YOUR OWN SHIP.
The wedges of immersion and emersion of an actual ship for
small angles of heel are practically sectors of a circle, and thus
resemble the wedges with which we have just been dealing, in
the vessel of cylindrical form, the wedges being exactly equal in
volume, and practically identical in shape, with their respective
centres at practically equal distances {x) from the vertical line
through the centre of buoyancy (tig. 85). So long as these con-
ditions remain unaltered, the vertical line through the centre
of buoyancy, at whatever angle the vessel may be inclined, will
always intersect the line a ft at the metacentre, and when such
is the case, the distance M G multiplied by sine of angle of heel
will give the lever of stability, G Z. But in vessels of ordinary
ship form when inclined to large angles of heel, the wedges of
immersion and emersion, although exactly equal to each other in
volume, are dissimilar in shape, with their centres at quite unequal
distances from the centre of buoyancy.
Metacentre Curves. — When this is the case, the vertical
line through the centre of buoyancy does not intersect the line
a b, fig. 85, at the metacentre.* For large heels the position of
the point M (originally the metacentre for the upright condition)
is more difficult to ascertain, and is, therefore, discarded in present
practice in determining the range of stability. Now, although it
is advisable for a seaman to thoroughly understand displacement,
buoyancy, the metacentre, and the principles governing and
affecting the same, yet it is not necessary for him to enter into
the mathematical method of calculating the same, for when these
matters are understood, every necessary information about their
values may be supplied to him in the form of curves, by the ship-
builder or naval architect who designs his vessel. Thus we have
shown in figs. 3, 5, 20, and 21 curves of displacement, curves of
"tons per inch," and also curves of centres of buoyancy. Since
these quantities are always the same at particular draughts, all
that the seaman requires are the curves themselves, the know-
ledge of their value, and how to read them. The same applies
to the metacentres. These also are fixed points for ea,ch draught
for the vessel in the upright position, and, as we have shown, for
small angles of heel. We shall now proceed to give an illustration
of such a curve, and show how it is constructed and read.
The principle of the calculation t for the metacentre of a vessel
at a particular draught is the same as for a box, except that on
account of the varying shape of the waterplane, a slight modifica-
tion has to be made, to find the moment of inertia of the water-
* The metacentre is a term which ought only to be applied to the point
M so long as it is constant in position, which is only for small angles of
inclination. t See Chap. a. for metacentre and other ship calculations.
STABILITY.
121
plane, which, divided by tlie displacement at the particular draught ,
gives tJie height of tJie vietacentre above tJie centre of buoyancii.
So that, first of all, we require the positions of the centres of
buoyancy. In fig. 20 a curve of centres of buoyancy is given
for a certain vessel. This we shall transfer to fig. 86, and set
oflf the metacentres for the same vessel.
[
%■
Scale of heights in ft. above bottom of keel.
The metacentres, as calculated, were as follows :—
At 4 feet draught, 10 feet above centre of buoyancy.
8 ,, 0-2
H
o
<
H
EC
CO
>
'A
<
H
Z O
00 '
6C CO
c
>}
))
»»
12
16
675
4
n
128 KNOW YOTJR OWN SHIP.
At the point in the horizontal scale of draughts, representing
4 feet draught, draw a vertical line intersecting the curve of
centres of buoyancy, and extending above it. Using the vertical
scale of feet at the side, set up the height of the metacentre above
the centre of buoyancy (19 feet), which shows the position of
the metacentre to be 22 feet above the bottom of the keel. The
same process is performed at the other waterlines, and when
all the points representing the metacentres have been set off, a
curve is run through them, which is that required, and enables
us to read off heights of metacentres at any draught.
Unlike the centres of buoyancy and metacentres, the centre
of gravity is not a fixed point except in certain conditions, and,
therefore, cannot be supplied to the ship's officer. Every varia-
tion in the arrangement of weight or cargo, whether it be a
yacht or cargo steamer, will affect the position of the centre of
gravity, since, as we have already observed, the centre of gravity
is the centre of weight. So that about the only conditions in
which the centre of gravity may be relied upon as occupying a
constant or fixed position, are, when — (1) the vessel is light, with
bunkers empty and no stores on board, (2) bunkers full, boilers
full, and all stores on board, and (3) in the case of cargo vessels —
the same as 2, with the holds jUled with homogeneous cargoes
which exactly bring them down to the load draught. To know the
position of the centre of gravity in conditions 1 and 2 is practically
all that is required for yachts, whether they be sailing or steam,
as these are about the only conditions in which they float. But
for vessels carrying miscellaneous cargoes, perhaps wheat on one
voyage, cotton on another, coal on another, and so on, the centre
of gravity may possibly after loading seldom occupy the same
position twice in succession, so that it becomes advisable to
ascertain the metacentric height under certain conditions of load-
ing. We shall, therefore, now endeavour to show how the ship's
officer may determine the metacentric height himself.
How to find the Metacentric Height and the Position
of the Centre of Gravity. — Perhaps some reader is imagining
that the method will be that described in the chapter on
" Moments," and it is quite true that the centre of gravity could
be found by striking a horizontal line at the bottom of the keel,
and multiplying each individual weight constituting the ship
and the cargo (shell plating, frames, floors, decks, beams, masts,
stores, cargo, engines, boilers, winches, windlass, and the host of
other items) by its height above the horizontal line mentioned,
and dividing the sum of the moments by the sum of all the
weights, the result being the height of the centre of gravity above
the horizontal line. If carefully done, the method would be all
STABILITY. 129
Very well, but the immense labour entailed must be evident to
every reader. Happily, an accurate, as well as a very simple
method may be adopted, by means of which the centre of gravity
can be determined in a very short time by experiment. The day
chosen should be as calm as possible. The vessel, lying either in
dock or river, should be moored only over stem and stern; no
ropes abeam, and, if possible, with what breeze there may be
blowing directly fore and aft, so as to lend no assistance in heeling
the vessel. Place a known weight with its centre over the centre
line of the vessel, as near as possible to midships, and capable,
when afterwards moved to the port or starboard, of inclining
her 5° or 6°.
This weight may consist of anything heavy enough in its
nature, and the centre of which and its weight can be accurately
determined. Pig iron* may be conveniently used, or blocks of
ballast iron, etc. These should be carefully ranged over as little
space, according to the size of the vessel, as possible, and may
weigh from 1 ton or less, to perhaps 15 or more tons.
This part of the operation having been carried out, the next
thing to do is to carefully note the draught at which the vessel
is floating. Let it be, say,
13 feet 6 jnches forward J ^ ^^^^ ^^^^^^ ^^ ^^ ^^^^^
This, on the displacement scale belonging to the vessel, reads
1400 tons (see fig. 3). At the centre line of the vessel suspend
two plumb lines, one forward, and the other aft. Let both lines
hang freely, and mark clearly a definite length on each of them,
measuring from the point from which each one hangs, in our case,
say, 8 feet. Great care should be taken to see that the lines
hang perfectly plumb on the centre line of the ship» Having care-
fully arranged all this, we can now proceed with the experiment.
Let the weight of (say) 12 tons be moved from the centre of
the vessel, first to starboard, as far as possible, in our example,
say, 14 feet. This distance of 14 feet is measured from the
centre of the weight when it was on the centre of the vessel to
the centre of the weight when afterwards moved to starboard.
Having done this, on going to the plumb lines it is found that by
the fore one a deviation of (say) 5| inches has occurred on the
length of 8 feet, but on going to the aft one the deviation is
found to be 6 inches. The weights should now be carried to the
port side, and placed at the same distance as on the starboard
side, 14 feet from the centre line of the ship. On going again
* A reliable and most convenieDt method is to fit a large fresh-water
tank on each side of the ship, and use the weight of water in this (if
sUffioient} for Inclining purposes.
I
130 KNOW YoUR OWN SHIP.
to the plumb lines it is found that by the fore one 61 inches
deviation has occurred, and 5f inches by the after.
If all these be added together and divided by 4, we shall have
the mean deviation : —
Port forward = 6J
„ aft = 5J
Starboard forward = 6^
„ aft = 6
4)23i
6 '875 inches. Mean deviation.
Having obtained this result, the practical part of the experiment
is now finished, the remainder being a matter of simple calculation.
Three results have to be found.
1. The distance the actual centre of gravity has moved to one
side. Perhaps some reader is saying, " but the centre of gravity
has not been found." True, nevertheless we can find how far it
has moved in the direction of the shifted weight. According to
our study of moments in Chapter II., the rule is : — Multiply the
toeight moved by the distance it is inoved, and divide the result by
the total weight.
Weight moved = 12 tons.
Distance moved = 14 feet, and the total weight equals the displacemeat,
which was found to be 1400 tons.
-— — - — = = 0*12 of a foot = distance the centre of gravity has
1400 tons displacement
moved in a line, parallel to the line joining the centres of the weight,
in its original and in its new position.
2. The next thing to be done is to find the cotangent of the
angle to which the vessel has been inclined. This is arrived at by
difoiding the length of tlie plumb line in incites by the mean deflec-
tion of the plumb line at that length in inches,
' = 16*3 = natural cotangent of angle of inclination.
Although it is not needed in this calculation, still by referring
to the table of cotangents at the end of the book, it is seen that
the vessel has inclined to a mean angle of 3^**.
3. The last part of the operation is to find the metacentric
height^ or the distance from the centre of gravity to the meta-
centre. This is done by muHiplying the shift of the centre of
gravity by the cotangent of tlie angle of heel,
0*12 X 16*3 ^ 1*95 feet, distance of metacentre above centre of gravity.
This result is the metacentric height of the vessel in its present
condition — that is, with the weight used for heeling upon the
STABILITY. 131
upper deck. Now it is not likely that this weight will be carried
in this position when the ship goes to sea. Should the weight be
placed on board simply for the experiment, with the intention of
placing it ashore afterwards, a correction must be made in the
metacentric height, for it is evident that the weight being as we
now find it, say, 8 feet above the centre of gravity, its eflfect is to
raise the centre of gravity higher than it would be were the weight
not there. Therefore, by taking the weight away, the centre of
gravity must be lower. Then weight removed, multvplied by its
distance from tJie centre of gravity^ and the result divided by tlie
total weight, which must be reduced by the removal of the weight,
will give us the distance the centre of gravity has lowered^
12 X 8 96
= 0*06 of a foot = how much centre of gravity is lowered.
1400 - 12 1388
Thus after the removal of the weight, the centre of gravity is
1-95 + 0*06 = 2-01 feet below the metacentre.
But suppose the weight used for heeling is one which is
intended to be kept on board, being perhaps part of the ballast
iron in the case of a yacht. Then, by lowering the weight into
the hold again, the eflfect must be to lower the centre of gravity,
and we proceed as in the previous case. (Weight x distance
moved -^ displacement = distance centre of gravity has lowered.)
Measure the distance from the centre of the weight on deck to its
centre in the new position it will occupy in the hold, say, 15 feet.
Then,
12 X 15
= '12 of a foot = distance centre of gravity is lowered.
Therefore the corrected metacentric height is
1-95 + 0*12 = 2-07 feet.
Having become acquainted with the points known as the centre
of buoyancy, the metacentre, and the centre of gravity, and to
some extent the causes affecting them, and having given some
attention to the wedges of immersion and emersion when the
vessel is inclined, we are now more capable of pursuing our study
of the subject, and of endeavouring to understand how the levers
and range of a vessel's stability are affected under greater angles
of heel.
Valuable as a knowledge of the metacentric stability (that is,
stability at very small angles of heel) of a vessel may be under
certain circumstances, yet it alone is no safe criterion of a vesseVs
resource of safety, when exposed to severe weather and subject to
excessive heeling forces.
132
KNOW YOtTB OWN SHIP.
For example, in the loaded condition one vessel might have a
metacentric height of, say, 1 foot, which for small angles of heel
would generally give good righting force, but for greater angles
of inclination the righting lever might rapidly decrease and soon
vanish altogether ; while another vessel, with perhaps only 6
inches metacentric height, and possessing small righting force for
small angles of heel, might yet have a very long range of stability
and good righting force at greater angles of inclination.
It thus becomes evident that further investigation is necessary,
and we have yet to discover those features in a vessel's design,
condition, etc., which so powerfully influence her stability under
all angles of heel.
No.
Dimeusions.*
L. B. D.
in feet.
o «•§
4) 0) S3
©^ I— I
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
100 X
100 X
100
100
100
100
100
100 X
100 X
100 X
100
100
100
100 X
100 X
100 X
100 X
100 X
12 X 10
15 X 10
20 X 10
25 X 10
30 X 10
20 X 10
20 X 10
20 X 10
X
X
X
20 X 10
20 X 10
20 X
12 X
X
X
X
20
20
20
10
10;
10:
;>
f)
5
5
1
1
2
4
.
(5 '
•gi^
sZ
O S '-
■S^^a
tn**^ .S
S.d a>
Centn
ravity
attorn
letace
Heig
inFe
0.5
fn
6-3
-•1
6-3
•67
(5-3
2
6-3
3-9
6-3
6-2
6-3
2
6-3
2
Kemarks.
8
12
30
30
10
10
10
10
4
1
1
1
1
1
1
1
6
6
6
6
6
6 I
6 '
16
6-3
6-3
6-3
8-05
7-3
4-3
2-3
6-3
5-3
6-3
14-5
2
2
2
•25
1
4
6
-•1
•9
6-2
6-2
Showing effect of increase
in beam, other dimen-
sions remaining un- i
changed.
Showing effect of increase I
in freeboard, other di-
mensions remaining un-
changed.
Showing eflfect of variations
in position of centre of ,
gravity, dimensions re- ;
maining unchanged. i
* L = Length ; B = Breadth ; D = Draught.
To treat of this effectively by means of actual ship stability
data, would necessitate such a graduated variety of vessels as to
make such a task a very laborious one. However, this difl&culty
is easily surmounted. Our purpose will be served by using
vessels of box shape, which, while simpler in form than actual
ships, are nevertheless capable of lending themselves to the main
features we wish to illustrate, and of proving the principles it
is desired to make prominent. The three great factors upon
which the stability of any floating objiect depends, whether it be
nmlt ol rishtliiii
134 KNOW TOUB OWN SHIP.
of ship or box form, are beam, freeboard, and position of centre of
gravity. By means of a series of box vessels, the particulars of
which are given in the table (p. 132), and the curves of stability
in fig. 87, the endeavour will be made to reveal the importance
of each.
1. Effect of Beam. — Vessels, numbers 1, 2, 3, 4, and 5, with
the curves of corresponding numbers, will serve for reference
and examples in this case. Here we have fiwe vessels, each 100
feet long, 10 feet draught, 5 feet freeboard, and with beams of
12, 15, 20, 25, and 30 feet respectively. In each case we have
imagined the centre of gravity to remain stationary at 6*3 feet
from the bottom of the box, for the depth and draughts being
assumed to remain the same in each vessel, it is quite reason-
able to take it for granted that no change would occur in respect
to the position of the centre of gravity.
It has already been shown, earlier in this chapter, that
increase of beam raises the metacentre. This has, therefore,
happened in the examples with which we are dealing, the result
being a metacentric height of -0*1, '57, 2, 3*9, and 6*2 feet
respectively.
Let us examine the curves of each of these vessels, and see
what can be gathered from them.
Curve No. 1 commences with the metacentre 0*1 foot below the
centre of gravity. In this condition the vessel is incapable of
floating upright. Will she capsize? The curve answers the
question most emphatically that she will not. If undisturbed
she would take a slight list and then lie at rest. If forcibly
inclined, the righting lever of stability would continue to grow
in length, until, when on her beam ends (90" on curve), she has
barely attained her maximum stability.
There is, however, nothing to elate one very much in the fact
that a vessel has splendid stability at 90** of inclination, for every
seaman knows that long before that angle is reached, it would
be impossible to stand upon or work such a ship, and, moreover,
weights on board which are considered as permanent and fixed
would be on the move, and then most disastrous results would
inevitably ensue. If the levers of stability are good up to 50°
or 60**, and even then are decreasing and vanish altogether at
90°, not much fear need be entertained, for rolling to angles of
even 30"* or 40" on each side is considered very excessive.
Had we been guided in this particular case entirely by the
metacentric height, the conclusion might have been come to that
her condition is much more serious than it actually proves to be.
Certainly the vessel is too tender ; but what is needed is either
ballast of some kind in the bottom, if the vesse} is not fjown to
STABILITY. 135
the load waterline, or else a re-arrangement of the cargo so as to
bring the heavy weights lower, and thus increase the metacentric
height. Either of these methods \vould add immensely to the
improvement of the vessel's condition. Further observations on
this type of vessel are made at a later stage, in the remarks on
"Rolling" and "Behaviour at Sea."
Curve No, 2. — The diflference between this vessel and the
previous one is, that owing to an increase of 3 feet in the beam
the metacentre has been raised, and now the metacentric height
is 0*57 foot. The curve shows longer levers of stability up to
90* of heel, where it crosses Curve No. 1. The vessel is there-
fore stiiFer, and has greater righting force up to this point, but
her maximum lever of stability is reached sooner than in the
foregoing vessel.
Curve No. 3. — The beam is now 20 feet, giving a higher
metacentre, and a metacentric height of 2 feet.
Curve No. 4. — Here the beam is 25 feet, with a higher
metacentre, and a metacentric height of 3*9 feet.
Curve No. 5. — In this case the beam increasing to 30 feet, the
metacentre continues to rise, and the metacentric height attains
6-2 feet.
Let us see what information can be gathered from these curyes
for similar vessels increasing in beam only.
First. With every increase in beam, and consequent increase
in the metacentric height, the successive curves rise steeper and
steeper, indicating greater stiffness and resistance to heeling.
Second. Each successive curve reaches a greater height than
its predecessor, giving a longer maximum lever of stability, and,
consequently, a greater righting moment.
Third. In each successive curve the maximum lever of stability
is reached at a smaller angle of inclination.
Fourth. In each successive curve the lever of stability
vanishes at a smaller angle of inclination.
Judging from these curves, we might at first be inclined to
give the entire credit of the great growth in the lengths of the
righting levers in each successive curve to the increased meta-
centrip height resulting from the increased beam ; but a further
comparison of curves will assist us in arriving at a more correct
conclusion.
2. Bflfect of Freeboard. — Curve No. 6. — The vessel repre-
sented by this curve has the same length, breadth, draught,
metacentric height, and height of centre of gravity above the
bottom of the keel as No. 3. Instead of 5 feet freeboard she has
only 1 foot. Mark the effect in the curve. Instead of the
splendid sweep of No. 3 reaching its maximum lever of 1*9
136 KNOW YOUR OWN SHIP.
feet at about 60' of inclination, and vanishing at considerably
past 90', No. 6 has never more than a lever of 0*2 foot, and that
at the angle of 20°, the curve vanishing altogether at an angle of
less than 50°.
Curve No. 7 is for a similar vessel, with 1 '5 feet freeboard.
>> " }> >» »> ^ »> >»
Q 4
a •'•^ »> )> »> " II )»
Let us gather again what these latter curves indicate.
Fi7'st Even good beam with good metacentric height, unless
combined with suitable freeboard, is no guarantee for either a
good range or good levers of stability. This is proved by a com-
parison of Curves Nos. 6 and 7 with Curve No. 3, and comparing
also No. 17 with No. 5. These two latter are also identical
vessels, with the exception of the freeboard, which is 1 foot 6
inches in the former and 5 feet in the latter. The great diiFer-
ence in the curves, which can only be attributed to the diiFerence
in the freeboard, is very apparent.
Second, Increase in freeboard with undiminished metacentric
height, increases not only the length of the levers, but the
maximum lever in each case is at a greater angle of inclination,
and the range of stability is lengthened out also. Curves Nos.
6, 7, 8, 9, and 10, with their increasing freeboard, prove this,
each of the first four in its turn approaching No. 3, until No.
10, with the great freeboard of 8 feet, far surpasses it in both
maximum levers of stability and range.
It may be all very well to make the statement that freeboard
has this and the other effect upon a vessel's stability ; but some
reader may be asking the question, " How is it that freeboard is
capable of producing such an effect 1 " An endeavour to explain
this will be made by the aid of the following graphic illustration
(fig. 88).
Figs. i. and ii. are the vessels in the table, Nos. 8 and 3
respectively. They are similar to each other, except that i. has
2 feet, and ii. 5 feet freeboard. Floating in the upright condi-
tion, they have exactly the same metacentric height, 2 feet.
Let fig. i. be heeled until the deck edge is down to the level
of the water, as shown in fig. iii., the angle of inclination
being 10°. To find the lever of stability we must turn our
attention to the centre of buoyancy. Let fig. x. represent
the buoyancy of the vessel, which corresponds in every respect
to the immersed part of fig. iii. The centre point in fig. x. is
B, and this is the centre of buoyancy. By transferring the
position of B to fig. iii., we see its position in relation to the
centre of gravity. The distance between the vertical linea
137
• •
vm
VII
1
1.
":&.- z. T
— -"
c
. —
— _ .
a
.0. _
a
1
1
1
■
Fia. 88,— fS^OWINO EJffllOT Of f'REBftOAUp ON STAfiJI^ITT,
138 KNOW YOUR OWN SHIP.
through these points is the lever of stability, and since it inter-
sects the centre line, P, above the centre of gravity, it is a
righting lever. Although the shape of the buoyancy has altered
in form under the inclination, owing to the transference of the
wedge of buoyancy shown by the hatched lines, to the other
side of the vessel, indicated by a black wedge, yet its volume is
unchanged. The centre of buoyancy, therefore, travels in the
direction in which the buoyancy is transferred, just in the same
manner as shifting a weight upon a lever, the distance in the
case of the wedges being reckoned from centre to centre.
Turning to fig. ii. with the greater freeboard, on inclining this
vessel to the same angle 10**, her deck edge is still considerably
out of the water (fig. iv.). However, in this condition her form
of buoyancy is similar to fig. iii., simply because the wedges of
immersion and emersion are identical in shape. The centre of
buoyancy, therefore, occupies the same position, and it follows
that the lever of stability must be similar to that in fig. iii.
Let fig. ii. be now heeled until its deck edge reaches the
waterline, as shown in fig. vi. The reasoning applied to ^g. iii.
will apply in this case also : — A wedge of buoyancy has been
transferred from one side to the other, giving the form of
buoyancy shown below the waterline, the centre of which is
the centre of buoyancy, B. This point again shows the relation
of the centre of buoyancy to the centre of gravity, and the
lever of stability is found to have increased simply because a
larger wedge has been transferred a distance of ^• to g (the centres
of the wedges from each other).
Fig. i. at this angle of inclination shows a different state of
affairs (see fig. v.). There is certainly a wedge of emersion, but
owing to the decreased freeboard, there cannot be a similar
wedge of immersion. The dotted line indicates the boundary of
the greater buoyancy of fig. vi. Now, supposing fig. v., when
inclined, to float at the waterline W L with the wedge of
emersion K, then there ought to be a wedge similar in volume
immersed. But this cannot be, for the immersed wedge is
deficient by the volume of the small wedge indicated by the
hatched lines in the diagram. Now, the volume of the emerged
part, of whatever shape, must equal the volume of the immersed
part, and since the immersed wedge is deficient by the small
wedge already referred to, this loss of buoyancy can only be
regained by the vessel sinking to a deeper draught, thereby
spreading thei buoyancy of the lost wedge along the waterline,
and thus causing the vessel to float at the new waterline wL
The black part in the figure shows the new immersed buoyancy.
The important '>T)oint is to fipd wha,t effect this new immersed
>
\
STABILITY. 139
buoyancy will have upon the lever of stability. The more
buoyancy that can be placed towards the side to which the
centre of buoyancy has already begun to move, the further will
this point be brought towards that side. Owing to the lower
freeboard the loss of the hatched wedge of buoyancy has robbed
the vessel of a most effective agent in bringing out the centre of
buoyancy from the centre of gravity, and by placing this lost
buoyancy along the waterline, a further check is made upon the
outward movement of the centre of buoyancy, and the tendency
is to draw it back again ; hence the decreased lever of stability,
as compared with fig. vi. Passing now to the conditions shown
in figs. vii. and viii., we find these vessels heeled to an angle of
90". The centre of buoyancy can easily be determined in these
cases. For fig. vii. it will be half the distance from the bottom
(not the bottom of the figure, but the bottom of the ship) to the
deck, which is — - — = 6 feet, and the centre of gravity being
6*3 feet, the result is an upsetting or capsizing lever of 0*3 of a foot.
Fig. viii., however, has the advantage of the buoyancy afforded
by the additional freeboard shown beyond the dotted line.
This naturally tends to draw out the centre of buoyancy, and its
position now is — = 7'5. 7*5-6*3 = 1*2 righting lever.
The foregoing remarks, with a little study of the figures them-
selves, will leave little doubt in the mind of the reader of the
importance of freeboard as a factor in affecting stability.
3. Effect of Position of Centre of Gravity. — Let us take
our final illustration, and note the eflfect of obtaining metacentric
height, not by means of increasing the beam, and thereby raising
the metacentre, but by retaining the same beam and same posi-
tion of metacentre, and lowering the centre of gravity.
This may be done to a considerable extent in merchant
steamers, in loading miscellaneous cargoes, by keeping the
heavy weights low, but to a very much greater extent can it
be done in yachts, where the centre of gravity can almost be
placed wherever desired by means of permanent ballast.
Cui-ves No8. 11, 12, 7, 13, and 14 are for vessels 100 feet long,
20 feet broad, and 10 feet draught, with 1 foot 6 inches freeboard,
the metacentre being, therefore, at the same height from the
bottom of each vessel — viz., 8' 3 feet. The only difference between
them is in the height of the centre of gravity.
For No. 11, the centre of gravity is taken at '25 foot below the metacentre.
>» ^^i it >i 1 I' >»
,, •» >» I) ^ leet ,,
>» ^^t >i it ^ >» >>
140 KNOW TOUR OWN SHIP.
The effect of this alteration in the position of the centre of
gravity is shown by the curves. Firsts at a particular draughty
by every downward movement of the centre of gravity, thereby
causing an increase in the metacentric height, both the levers and
range of stability are lengthened. Second, each curve rises more
steeply than its predecessor, indicating greater stiffness.
We have already seen the effect of beam upon stability.
Suppose 10 feet be added to the beam of a vessel identical in
every respect with No. 14. The effect is to raise the metacentre,
and give much greater metacentric height. But let the centre of
gravity also be raised from 2*3 feet from the bottom of the vessel
to 6*3 feet, the metacentric height being now 6-2 feet, the result
is to give a vessel identical with No. 17. Nos. 14 and 17 differ
now practically in beam only.
An error is sometimes made in a case like this, it being
imagined that the broad vessel, even with the same metacentric
li eight, is better than the narrow one of the same depth and
freeboard. If the curves of these two vessels be compared, their
stability is seen to be widely different, the narrow vessel possess-
ing more stability in every respect than the beamy one, except
perhaps at the beginning of the curve.
Now how does this happen ? In the first place, the advantage
of the increased metacentric height, which was obtained by the
increased beam, was robbed from the vessel by raising the centre
of gravity, and making the metacentric height similar in both
cases. Perhaps some reader is still saying — " Having made the
metacentric height similar for both vessels, why are the curves
not similar?" This is just where the error is often made in
depending upon the metacentric stability, which, as has been
previously stated, is no guide for a vessel's range of stability,
but only for small angles of inclination. Up to 7° or 8° these
curves are approximately the same. For gi*eater angles of in-
clination, we must turn our attention to the centre of buoyancy,
and trace its movements in relatioa to the position of the centre
of gravity.
In A and B, fig. 89, no levers of stability are seen, since the
vessels float upright and are perfectly stable, with the centre of
gravity, centre of buoyancy, and metacentre (the last not indi-
cated) in the same vertical line, a h. In figs. C and D the same
vessels are inclined to angles of 45**. It is now seen that the
levers of stability in this condition are very different, those for
tlie smaller vessel being much the greater. Both the centre of
buoyancy and the centre of gravity, though chiefly the latter,
are accountable for this result. Turning our attention first to
tUe centre of buovancv, we ftnd that, in both figs. C apd D,
STABILITY.
141
CL
CU
B
^
.'S
b^
C
B
—a^
F,-~
K
B
! I
Of
Fig. 89. — Comparison of Vessels with different Beams but similar
Metacentric Heights.
142 KNOW YOUR OWN SHIP.
owing to the small freeboard in each case, the deck edge has
become immersed when inclined to a very small angle. This at
once checks the outward movement of the centre of buoyancy
though fig. C, owing to its smaller beam, has the advantage to
some extent, since greater inclination would be needed to immerse
its deck edge than would be required for fig. D.
Turning now to the centre of gravity in each case, we find here
the chief factor in producing the great dijfference in the stability
levers. It is first noticed that their difference in position from
the bottom of each vessel on the line a & is very great, although
the metacentric heights in the upright condition are practically
identical. In fig, B it was easy to get a good metacentric height,
owing to the great beam, but in fig. A the greatly reduced beam
made it necessary to very much lower the centre of gravity, in
order to get the same metacentric height. Hence the difference
in their positions. It will also be observed that the lower fJie
position of tlie centre of gravity is on the line a b, the greater
viicst be the righting lever of stability (a glance at the figures
will show this clearly), and on the other hand, the higher the
position of the centre of gravity on the same line, the smaller
the lever. This, then, accounts to a great extent for the difference
in the levers of stability. So that even on their beam ends, at
angles of 90**, we still find the narrower vessel (fig. E) with a
large righting lever, while the broader one, F, has actually an
upsetting lever.
However, the case we have taken is certainly an extreme one
for cargo or passenger vessels, for while in the broad vessel the
position of the centre of gravity would very often be found high
in comparison with the depth, in the narrow vessel, it would be
impossible to load her and have the centre of gravity as low in
comparison with the depth. Were the two vessels loaded in the
same manner — that is, in relation to the vertical position of the
weights of the cargo, the centre of gravity in both vessels
occupying the same position from the bottom of the box
— a vastly different result would arise. Let the centre of gravity
of the narrow vessel be raised by the loading of cargo to the
same position as in the broader one — viz., 6*3 feet from the
bottom of the vessel. The dotted lines on the figures show the
new vertical line through the centre of gravity of the nari'ow
vessel, and curve No. 7 will show the whole range of stability.
The tables are now turned against the narrow one, indicating
much reduced stability. Hence the necessity of wisdom in load-
ing, as, in the latter ifease, the heavy weight of the cargo would
have to be placed muclr*. lower in order to get anything approach-
ing similar levers of stabSity for the two vessels.
\
STABILITY.
143
But while the position of the centre of gravity at 2*3 feet from
the bottom of the vessel for curve No. 1 4 is an exaggerated case
for merchant vessels, it is by no means out of the way for sailing
yachts, for m order to get great stiffness and long levers of
stability, which are necessary to carry great sail area, especially
with small beam, the method of bringing the centre of gravity
very low by placing ballast either in the keel, or else as low as
possible, has to be adopted.
Before leaving this part of the subject of stability, the reader
IS again warned against jumping to the conclusion that even a
.5^
SB
go
•— V -
1
so'
'AO'
70'
— T—
SO
— 1
.9/7'
CC
Scale of angles of inclination in degrees.
Inclination showing maximum lever of stability.
Curve of stability for a sailing ship, 270 feet long, 41 feet beam, and 26 feet 3 inches
depth, in a light condition, with about 112 tons of ballast on board. Metacentric height,
2-tt feet. Centre of gravity, 20^ feet above the top of the keel. Freeboard, 17i feet.
FlO. 90.
combination of good beam, good freeboard, and good metacentric
height will always produce satisfactory stability. This has
already been shown by the several box vessels and their curves,
and will further be emphasised by a glance at the curve of
stability (fig. 90), which is for a sailing ship in a light condition.
She has 41 feet beam, 2*9 feet metacentric height, and 17^
feet freeboard, the last of which is extremely great, and yet
the curve of stability in this condition represents both short
levers and very short range, this being attributable to the fact
that, in the light condition, the heavy top weight of masts,
spars, etc., brings the centre of gravity very high, and it haa
144 KKOW tOtJJft OWN SHlt».
already been pointed ont that the higher the centre of gravity,
the shorter are the levers of stability, and the sooner does the
vertical line through the centre of buoyancy intersect the centre
line of the ship below the centre of gravity, thereby creating a
capsizing moment. The same vessel in her loaded condition,
with only 5J feet freeboard and 3 feet metacentric height, would
have both immensely greater levers, and greater range of stability,
because then the centre of gravity is much lower in its position.
In a box vessel, say, 20 feet deep, if the centre of gravity be
at half the depth, the righting Jever of stability must vanish at
90** of inclination, whatever be the freeboard, since in this con-
dition the centre of buoyancy and the centre of gravity are in
the same vertical line. If the centre of gravity be higher than
half the depth, the levers will be shorter and the range less also,
but if the centre of gravity be lower than half the depth, then
the levers will be longer, and the range will extend beyond 90**
of inclination. Now, all actual ships are not of box form, though
it is granted that in some cases it is somewhat difficult to draw
that distinction. Of two vessels of similar beam and depth, the
one with most buoyancy in the upper half of her depth, being
therefore most fined away at the bilge and bottom, can afford
to have the centre of gravity the higher, and the nearer the box
section is approached, the lower must be the centre of gravity.
The actual box ship is, therefore, the worst case, since it
brings the centre of buoyancy into the lowest possible position ;
and, on the other hand, the vessel fullest at the waterline, and
well fined away below, has its centre of buoyancy in the highest
possible position, in which position the longest levers and the
greatest range of stability are produced, other features in the
design being favourable. It is thus impossible to stipulate a
particular position for the centre of gravity applicable to all
ships.
For a box-shaped vessel, if the centre of gravity is from about
0*5 to 0*6 of the depth from the top of the keel, with fair meta-
centric height, a fairly good range of stability may be expected,
though the righting levers may be small under certain circum-
stances. For vessels of finer underwater form greater stability
would be developed, and when the centre of gravity is less than
0'5 of the depth from the top of the keel, great stability may be
anticipated.
Effect of Tumble Home, — In fig. 91, let G be the centre
of gravity, B the centre of buoyancy in the upright posi-
tion, CDE the immersed wedge, and K the centre of the
immersed wedge.
The greater the distance from the original centre of buoyancy,
STABILITY. 145
B, to the centre of buoyancy of the immersed wedge, K, as
shown by the line P, the greater will be the eiFect in drawing
the centre of buoyancy out from its original position. Let B'
be the new centre of buoyancy when inclined, and GZ the
righting lever of stability.
Now, supposing a piece of the shape of the black wedge be
cut oflf from the vessel, let us observe the eflfect upon the
stability. Owing to the loss of this buoyancy when inclined,
compensation must be made by apparently drawing upon the
reserve buoyancy, and taking a layer off all along the waterline
to the dotted line, simply because the wedge of immersion is
now less than the wedge of emersion ; and they are equalised by
adding a layer to the wedge of immersion at C D, and deducting
a layer from the wedge of emersion at W C.
The centre of the immersed wedge, K, will have travelled
Fio. 91.— Effect of Tumble Home on Stability.
towards the left of the figure, causing B' to move in the same
direction, and the layer of buoyancy along the waterline, W to C,
will also have aided to produce this effect.
6Z will now have become shortened, which means reduced
righting moment of stability.
Taking the case of a vessel *of ship form, we can easily see the
applicatioi\ of the above illustration. Instead of carrying the
sides up perpendicularly they are usually curved in, as shown
in fig. 15. This is known as tumble home. A valuable piece
of buoyancy is lost ; in fact, the very part of the wedge which
is most efficacious in drawing out the centre of buoyancy from
the centre of gravity is cut away. Thus in vessels of low free-
board, and especially if at the same time possessing narrow beam,
the effect of much tumble home may be to assist in causing
deficient stability in certain conditions. However, as it is not
usual to give an ordinary mercantile vessel more than a few
U6
KNOW YOUR OWN SHIP,
inches of tumble home at the main deck, the effect is not serious
in the ordinary types of modern broad beamed cargo steamers.
&
g
«>
•a
o
03
Scale of Angles of Inclination in Degrees.
Curves of stability for a cargo steamer— Length, 480 ft. ; beara, 67 ft. ; depth, 40 ft.
Curve No. 1, Light condition, metacentric height, 2 68 ft.
2, Load „ „ 3-67,,
»>
Scale in Degrees.
Curve for a steamer 410 ft. long, 50 ft. 6 ins. beam, 32 ft. depth.
No. 1, Light condition, metacentric height (G M) = 11-06 ft.
No. 2, Loaded with homogeneous cargo, 7 ft. 6 ins. freeboard, G M 1*85 ft.
No. 3, Same as No. 2, with coal consumed. G M 1-68 ft.
Note.—l ft. in the scale of levers in this figure is equal to 2 ft. for No. 1 Curve. The
levers are thus only half length on this diagram.
00'
W
80'
ito
30 ^o' SO'
Scale in Degrees.
Curve for a vessel 360 ft. long, 45 ft. beam, 30 ft. 1 in. depth. Metacentric height, 1*48 ft.
Figs. 92, 93, and 94 are Examples of actual Ship Curves.
A point which is sometimes overlooked on the part of the
owner or his representative in the design of a new vessel, is the
value of sheer. TUut it adds to the uppearauce, gives valuable
STABILITY. 147
rising power, and tends to prevent the shipping of water over
the stem and stem, must be clear to everyone.
But one of its best features is that it produces increased free-
board, the use of which has already been discussed.
Stability in difterent Types of Vessels. — As regards types
of vessels best adapted to produce good stability when of suit-
able dimensions, and the loading properly carried out, those
with most freeboard must come first.
Thus we have the awning-deckery with its completely closed-in
light superstructure between the main and awning decks,
splendidly adapted for carrying passengers or light cargoes.
Next comes the spar-decker with a stronger superstructure,
and adapted for carrying cargoes of greater density with smaller
freeboard in comparison with the awning-decker.
Last, we have the strongest type of ship, the two or three
decker. This is the best deadweight carrier, having least freeboard.
Unfortunately, structural strength and stability are in no way
related to each other, and thus, as statistics prove, especially the
older types of these vessels, with their small beam to depth, and
also small freeboard, have produced the most disastrous results,
through lack of stability. A vessel which has found great favour
among shipowners during late years, because of its special adap-
tation for certain trades, is the raised quarter-decker^ which is
simply a modification of the strong two or three deck type pre-
viously referred to, and whose comparatively greater freeboard
assists in producing more favourable stability. (See also page 192
for further remarks upon types of vessels, etc.)
Note, — Awning- and spar-decked ships are equally as strong as three-
deckers in relation to the deadweight they carry at their respective load lines.
H8 KJ^OW TOUR OWJT SHIP
CHAPTEK VI. (Section II.)
ROLLING.
Contents. — Rolling in Still Water — Relation of Stiffness and Tenderness
to Rapidity of Movements in Rolling — Resistances to Rolling — Danger
of great Stiffness — Rolling among Waves — Lines of Action of Buoyancy
and Gravity — A Raft, a Cylinder, and a Ship among Waves— Syn-
chronism, how Produced and Destroyed — Effect of Loading upon
Behaviour — Effect of Transverse Arrangement of Weights upon Rolling
Motions — Alteration in Behaviour during a Voyage — The Metacentric
Height — Fore and Aft Motions — Fore and Aft Arrangement of Weights,
Boiling. — After the consideration already given to the subject
of stability, we are now able to proceed further, and observe the
relation between stability and rolling at sea, and what means
can be adopted to reduce the latter to a minimum.
Rolling is often spoken of as though it were a particular
quality belonging to a ship. For instance, it is not uncommon
to hear a ship described as a heavy roller ; or another, as being
very steady. A little investigation will show that it is not
strictly correct to so characterise any vessel. At the same time,
however, we shall see that the design of some vessels lends more
encouragement to rolling than others; and, on the other hand,
it is possible to a considerable extent to overrule even the
influence of design, and make a vessel either steady, or specially
inclined to heavy rolling, in spite of design.
Let us briefly enumerate the points we have already studied,
which will help us.
First, — If a vessel rolls under the influence of some external
force, the power she possesses which brings her back to the up-
right is her stability.
Second. — If a vessel has a great metacentric height, it follows
that, at least for small angles of inclination, she possesses con-
siderable righting moment, and the curve representing levers of
stability will rise the more steeply the greater the metacentric
height. Such a vessel is said to be stiff.
Third, — If the metacentric height is small, the reverse of the
previous case will be the consequence, the righting levers will
"be stiiall for small angles of inclination, and the curve of
stability will rise slowly.
The effect of metacentric height in relation to rolling is exactly
the opposite to what one would at first imagine. The stiff ship
with great metacentric height offering great resistance to inclina-
tion, is the very one which generally rolls most in a seaway ;
and the tender vessel, with small metacentric height and small
resistance to heeling, is usually the steady one. How comes
this ? We shall be better prepared to answer if we make a few
mental experiments upon a vessel for ourselves.
Rolling in Still "Water. — Let us imagine a ship with large
metacentric height and a fair range of st^ability to be lying in
the dock. By means of some external force let the vessel be
heeled over to, say, 10" of inclination, and held there. We
know that the centre of buoyancy will have shifted into the
centre of the new shape of displacement, and there is now
created a lever between the vertical lines passing through the
centre of gravity and the centre of buoyancy. It is, therefore,
evident that the vessel possesses an amount of righting force
exactly equal to the external heeling force required to so heel
her, and by means of which, when the latter is removed, she
will come to the upright. In this position the available right-
ing moment will have disappeared, since the centre of gravity
and the centre of buoyancy are again in the same vertical line.
Moreover, the greater the metacentric height the greater the
amount of available righting moment, and thus the more rapidly
will she reach the upright position.
Resistances to Rolling. — Let us now free our vessel lying at
the angle of 10°. The result is, that in the space of a few seconds
she has reached the upright. But does she remain there ? Not
at all, for just as in the case of a pendulum in travelling from
an angle of inclination to the vertical, an amount of energy of
motion {kinetic energy) is accumulated, which carries her over to
the other side, where again a righting lever is created acting in
opposition to the last roll. Were there no resistance of any
kind this process of rolling would be endless; but experience
shows us that after a series of rolls, the vessel will come to rest.
This is brought about by the united action of several kinds of
resistance.
First — T\\Q friction of the air upon the exposed surface of the
vessel.
Second. — The friction of the water upon the immersed surface.
Third, — Head resistance, caused by projections on the immersed
surface.
Fourth, — Wave resistance.
15()
KNOW ¥otJfe oWiJ sMii^.
As the great object is to get a safe and steady ship, let us Bfee
how far it lies in our power to modify these resistances.
Nothing can be done to increase the air friction, unless it be
by means of sail, which will certainly tend to produce steadiness.
It would be an easy matter to make a rough skin upon a vessel ;
but this would deduct so enormously from the speed, that it is
preferred to get the smoothest surface possible. In the third
case, however, a very great deal may be done to produce steadi-
ness by fitting projections in the form of keels or bilge keels.
The day of doubt as to the efficiency of this means is past. Not
only are naval experts agreed, but the testimony of every seaman
who has experienced the efficacy of bilge keels, especially when
fitted upon vessels which had previously been without them, is
unanimous as to their great value in reducing both the number
and angles of roll, or osciUations.
By an oscillation is meant a complete roll from port to star-
board, and the time occupied to perform such oscillation is
termed the period of oscillation. An example, taken from the
experiments of the late Mr. Froude, upon the model of the war
vessel "Devastation," will serve as an illustration in passing : —
Number and Descriptiou of
Bilge Keels.
1. No bilge keels, . ' .
2. One 21 inch bilge keel on each side,
! 3. ,, 36
4. Two 36
5. One 72
i>
II
>>
II
}i
II
Number of double
Oscillations before
Vessel was
brought to rest.
3U
12i
8
4
Period of double
Oscillation in
seconds.
177
1-9
1-9
1-92
1-99
In speaking of wave resistance, we do not refer to sea waves —
for, as was formerly stated, the vessel upon which we are experi-
menting is supposed to be lying in a dock — but to waves created
by the vessel in her rolling movements in the water. Such
might at first appear to be very trivial, but to create such waves,
even though very small, means an immense expenditure of
energy, and this, therefore, must be deducted from the total
available energy, which incites the vessel to roll. The combined
efiect of these agencies is to diminish the angle of inclination,
and, finally, to produce extinction. A noteworthy point to be
observed, as shown by the above table, is that for moderate
angles of inclination the period is approximately the same for
the larger as for the smaller oscillations. Thus we see that it
ROLLING. 151
is great stability which conduces to rapidity of rolling motion,
though not necessarily to great angles of inclination.
Danger of great Stifl&iess. — The danger of very stiiff vessels
with good range of stability is, not that they will capsize, but by
the severity of their movements that they will damage them-
selves by straining the structure and causing leakage, or by
shaking their masts overboard, not at all an unheard-of-occur-
rence, where broad-beamed sailing-ships, owing to pure ignorance,
have been ballasted in a manner producing enormous stiflfness.
On the other hand, the vessel with the small metacentric
height, when forcibly inclined to the same angle of 10°, and then
set free, returns to the upright much more slowly, having shorter
righting levers, and, therefore, less stored energy. The energy
of motion acquired in returning to the upright is less, and adding
to this the resisting agents, it follows that the angles to which
she rolls, and the number of oscillations before coming to rest,
will be reduced.
The nearer the immersed portion of any object approaches the
shape of a circle, and the nearer the metacentre and the centre
of gravity are together, the less power to regain the upright will
it possess until we reach the minimum in the actual cylindrical
type with the centre of gravity and the metacentre coincident.
Vessels of this latter type possess no righting force at all, and
thus, when inclined to an angle, they remain there, even though
entirely free. A very small external force, therefore, will heel
them, and turn the underside uppermost altogether.
Rolling among Waves. — Now the question arises, since the
motion of rolling is so governable, is it better to have the steady
type of ship with small metacentric height, or the stiff one with
great metacentric height ? But this we shall better answer if we
first briefly consider her more complicated motions among waves,
as thus far our considerations have dealt exclusively with vessels
in still water. Here, however, peculiarities arise, and although
the principles deduced from forced rolling in still water still
hold good to a great extent, we shall find our ship behaving very
differently at times from what we should imagine if we depended
solely upon our knowledge of rolling in still water. In the first
place, it is scarcely necessary to inform any reader who has ever
noticed a piece of wood floating in the sea among unbroken waves,
that it is not the mass of water composing the waves which
moves onward, but the form only. A slight forward and back-
ward motion of the floating object shows that the only move-
ment of the wave water is slightly forwards and backwards.
At a comparatively small distance below the surface of the water
there is apparently no motion whatever. An old, though not
152
KNOW YOtJft OWN SHIP.
strictly correct, illustration is that of wind blowing over a field
of corn, causing a waving motion as the heads incline with the
gusts of wind, and then rise again.
Raft, — As a complex form like a ship is a form more difl&cult
to deal with than that of a flat floating piece of wood, let us
examine, first, the behaviour of a small raft. In smooth water
we know that, owing to its great stiffness, its oscillations are
exceedingly rapid and its period very short, and that a condition
of rest is soon obtained.
We have also noticed that, when among wave water (figs. 95 and
100), its deck is always parallel, and the mast perpendicular to the
surface of that part of the wave upon which it is floating. It is
LENgr H . or Wave. ^
Fig. 95. — Behaviour of a Small Raft among Waves.
therefore upright on the summit and in the trough of each wave,
and its greatest angle of inclination is at about half the height
of the wave where the slope is greatest. In this case the raft,
being very small, behaves practically as though it were actually
a particle of the surface wave water. Such agreement becomes
less and less as the beam increases relatively to the length of
wave, as it can no longer lie flat on the surface, or have the
greatest angle of inclination where the wave slope is greatest,
until at last, where exceptionally large beams are reached, as in
the Czar of Russia's yacht "Livadia" (153 feet), the vessel no
Fig. 96. — Illustrating a very Beamy Vessel among Wavf^.
longer takes of the motion of a small raft at all, but maintains
a comparatively horizontal deck, as in fig. 96.
The longer the waves are in comparison with the breadth of
such a vessel, the greater inclination she would reach in
endeavouring to follow the angle of the wave surface. But in
a short sea she would be practically steady.
Cylinder, — Let us take as another example a vessel of the
cylindrical type.
ftottlKO.
153
In fig. 9? we see the object as it would float in smooth
water. Being of wood, and of equal density throughout, the
centre of gravity is in the centre, as is also the metacentre.
The centre of buoyancy is in the same vertical line through
this point, and the object floats at rest, as it will do at any
angle of heel, since it never has any stability ; a state which can
only exist when there is no righting lever, the vertical lines
through the centre of gravity and the centre of buoyancy always
coinciding.
In fig. 98 we see the same object among waves, and on a
wave-slope. Let us examine its condition now.
From observation every reader knows that no revolving or
heeling motion occurs. The line ah remains vertical, and the
—B
Fig. 97. — Behaviour of a
Cylindrical Vessel in
Smooth Water.
Fig. 98. — Behaviour of a Cylindrical
Vessel among Waves.
waterline varies from R S, when floating in still water, or on the
crest, or in the trough of the wave, to XY, the greatest wave-
slope. But on examining the object on the wave-slope, it is
found that the centre of buoyancy has shifted into the centre of
the imm^ns^d part. If we drop a vertical line through the centre
of gravity and through the centre of buoyancy, we see that these
points are no longer in the same vertical line, but that a distance
exists between them. If this distance represents the length of
the lever of stability, the vessel cannot remain in this condition
without making some effort to bring the centre of buoyancy and
the centre of gravity into the same vertical line, which effort
must incline the vessel more or less. But observation proves
that such is not the case, for the object makes no movement to
the one side or the other, the only interpretation of such
behaviour being that no lever whatever exists, and that the
downward force of the weight of the ship and the upward force
154 ki^oW IrouR OWN stiii^
of buoyancy are evidently being subject to other forces causing
them to act differently from the manner in which we have been
accustomed to consider them in still w^ater. It is just on this
point where many of those, whose knowledge of the subject of
stability, etc., is very limited, are apt to come to a wrong con-
clusion regarding the behaviour of ships among waves.
It is this apparently contradictory behaviour of ships which
has given rise to so many theories on the subject. But it was
not until the late Mr. Froude brought forward the now generally
accepted wave theory that so much light has been thrown upon
the subject. To discuss at length the theory of deep sea waves
would form a volume in itself, and therefore lies outside the aim
of a book such as this. Those wishing to pursue this branch of
the subject can find ample information in the volumes of the
Institute of Naval Architects, and also in the admirable works
mentioned in the preface. We can, however, make a few brief
observations, borrowing from the theory mentioned, such
principles as may be of assistance to men of practical experience
at sea, the class of men which it is the chief aim of this work to
assist.
A feather in the air would fall in a straight line to the earth
if there were no wind, owing to gravitation. Such fall, however,
is always more or less overruled by the force of the wind when
wind is blowing. Again, an iron plumb ball suspended from a
cord, would hang vertically, if undisturbed, owing to the down-
ward attraction of gravitatioa On approaching it with a magnet
sufficiently close to produce induced magnetism, gravitation is
interfered with, and the iron ball seeks to follow the magnet.
These instances are related simply to show that under certain
circumstances the power of gravitation (such as causes the weight
of a ship to act through its centre of gravity in a vertical line)
can be over-governed by the introduction of other forces. Thus
in waves we have what is termed centrifugal force^ which, acting
along with the gravitation force, gives a resultant force approxi-
mately perpendicular to the wave surface."* Turning to fig. 98,
* If centrifugal force were approximately perpendicular to the wave surface,
the fluid pressures in waves could not possibly be perpendicular to the wave
surface also, for gravity would show itself by producing a resultant which
would certainly not be perpendicular to the existing wave surface, but con-
siderably deflected from it ; but this is impossible, since the wave surface at
any point, at any moment, is perpendicular to the instantaneous resultant of
several forces, of which the centrifugal force is one.
Referring again to fig. 98, though the cylinder is on a wave slope, gravity
still acts vertically through its centre of gravity G, and were gravity the only
force exercising any influence upon the cylinder, it would cause the cylinder
to slide down the wave slope, biit this does not happen, for here again we find
that the natural vertical force of the weight of the cylinder is interfered with
i^oLLitTG.
155
We can now better understand how it happens that no righting
lever was set up, the reason simply being that the lines of action
Deck almost parallel to wave-slope,
with lines of action through G and B
practicaUy coincident. This is the
virtual upright.
Fig. 99.— Behaviour of a Ship among Waves.
through the centres of buoyancy and gravity coincided, as shown
by the arrowed line.
by the internal wave forces, producing a resultant which is the virtual upright,
approximately perpendicular to the wave surface, and therefore parallel to the
resultant buoyancy pressures in the wave. Thus an instantaneous position of
equilibrium is set up without any tendency whatever for the cylinder to slide
down the wave slope.
Where the water surface is horizontal, the buoyancy pressures act in
upward vertical lines. This is as true for the smooth surface of the vast
ocean as for the water in a bucket. And even when waves have been
created, the upward pressures from the ocean depths are in nowise changed.
But on coming to the actual waves themselves (which are only surface dis-
turbances extending to a very small depth as compared with the depth of the
ocean), we find that the buoyancy pressures are now exerted in lines of action
approximately perpendicular to the wave surface.
It is not supposed that this theory, known as the *' Trochoidal Wave
Theory," covers the whole question of wave forms at sea. But it is at least
a good working hypothesis for simple waves in very deep water, and has the
advantage of covering all forms oetween the two *' limits" of trochoids,
viz., the cycloid and the straight line, the last being, of course, smooth water.
The centrifugal force is perpendicular to the wave surface at the crest, and
acts directly in opposition to the universal gravity force, which we can never
leave out of account. Whatever influence this may have in reducing the
weight of the particles of wave water, it does not deflect them from the
vertical line. At the wave hollow the centrifugal and gravity forces also act
(this time together) in a vertical direction. In no other positions than wave
crests and hollows does centrifugal force exert itself perpendicularly to the
wave surface. In all other parts of the wave surface, its force acts more or
less obliquely, and gravity, as it always does, acts vertically, the resultant of
which two forces (together with any other less important yet possibly existing
forces) is approximately square to the wave surface. And thus the original
lines of buoyancy pressures, which were vertical in still water, are continually
changing the direction of their lines of action in wave water. (Sec fig. 100.)
kitoW fcftiA om amp.
ROLLING. 157
The short, dotted lines, perpendicular to the immersed surface of the vessel,
indicate the water pressures. The longer dotted lines, approximately per-
pendicular to the wave surface, indicate the direction in which the action of
buoyancy is exerted. These lines likewise indicate the virtual upright. When
a vessel floats with its deck parallel to the wave surface, the line of action
through the centre of buoyancy passes through the centre of gravity, and no
righting lever exists under such circumstances (see first position in the figure,
and also the first position in fig. 99).
Position 1 shows the vessel upright, when the hollow of the wave reaches
her. The lines of action of gravity and buoyancy are vertical
and coincide, and the vessel possesses no tendency whatever to
incline to the one side or the other*
Position 2. Here the wave has advanced and the vessel is upon the slope.
The direction of the buoyant action has changed, and the line
through the centre of buoyancy does not pass through the
centre of gravity. The righting lever now existing (the distance
between the parallel lines passing through 6 and G) tends to
bring the vessoPs masts pei'pendicular to the wave surface.
Position 3. The vessel is now upon the wave crest. Here she is still lagging
behind in her efiForts to rear herself perpendicular to the wave
surface, and instead of being upright she is considerably in-
clined. The distance between the parallel lines through B and
G indicates the righting lever.
Position 4. Here the vessel is upon the other slope of the wave, having only
succeeded in reaching the vertical position. Considerable right-
ing lever exists, as shown, still tending to bring her perpendicular
to the wave surface.
Position 5. The righting moment produced in position 4 creates a momen-
tum, which, by the time the vessel reaches the wave hollow
(position 5), has carried her beyond the vertical — in this case
the perpendicular to the wave surface. The righting lever is
again indicated.
The raft, being very stiff, and therefore much more rapid in its movements
maintains a condition always perpendicular to the wave surface.
168 KNOW YOUR OWN SHIP.
In dealing with a cylinder of no stability, we must not forget
that the least external effect of wind or water washing over it
might make it revolve ; the only resistance offered to this would
be the friction of the water on its immersed surface. In the
instance we took as an example, we considered it as not affected
by any external force, but simply under the influence of the
unbroken wave water. Now a modem ship is neither like a
raft nor a cylinder, yet it includes in some measure the quali-
ties of both, and may approach either in behaviour.
Ship, — Let us continue our experiment, and, placing an actual
ship among waves, watch her behaviour (figs. 99, 100). If she is
very stiff indeed — that is, has great metacentric height, with her
still-water rolling period less than half that of the waves she is
among, she will act very similarly to the raft, which makes two
complete rolls on a single wave. Supposing her to be floating in
the upright position, immediately the base of the wave reaches
her, she will at once seek to keep her masts perpendicular to the
wave surface. As the wave passes under her, she will reach, or
approximately reach, her greatest angle of inclination on the
steepest part of the wave-slope ; she will be upright at the
summit, and again upright in the trough. She will, therefore,
make two complete rolls in passing a complete wave (summit to
summit). Her greatest angle will always occur approximately
where the wave-slope is steepest. So that the danger in such a
ship would lie not in capsizing, for she scarcely ever expends any
of her stability, but owing to the rapidity of her movements, to
shift the cargo, or strain her structure.
Synohronism. — But let us suppose that our vessel is tender,
possessing a small metacentric height and long rolling period.
When the wave reaches her and passes underneath, she will
endeavour, as did the other ship, to rear . herself perpendicularly
to the wave surface. But we observed in our remarks upon
rolling in still water that she moves slowly, and so she cannot
keep up with the rapid motion of the wave, and falls behind.
Thus, by the time the steepest part of the wave is under her,
she is still at a considerable distance from that angle. Immedi-
ately that point is passed, the less inclination of the wave, as the
summit is approached, checks the heeling influence, and at the
summit the tendency is to bring her to the upright again.
However, here she is yet lagging behind the wave, having still
some inclination. When the other slope of the wave is reached
she has possibly just reached the upright, and, before she can
heel far under its inclining influence to the other side, the
trough is reached, where the tendency is to bring her to the
upright. We see then, that, by her slower movements, she lags
BOLLING. 159
behind the wave, and never reaches the angle of the greatest
wave-slope, and at the summit and the trough is generaUy
still inchned, not having reached the upright. Taking two
such ships upon a single wave, the stiff vessel with the great
metacentric height will always reach greater angles of inclina-
tion than the tender one with the small metacentric height,
simply because, as we have shown, the stiff ship can better
follow the angle of the wave ; while the tender one of slower
motion cannot reach the greatest angle of the wave on the one
side of the slope, while, after the wave has passed beneath her,
the other slope tends to push her back, and heel her to the
opposite side. But, although the passage of the first wave may
not have the effect of producing any great angle of inclination,
owing to the usually slower movement of the ship in comparison
with the speed of the waves, or more properly speaking, the
longer double roll jpenod to the wave period, it must be clear
that a time may come when a ship may reach her greatest
angle of inclination when the greatest angle of wave-slope
reaches her. The result will then be, that a comparatively
sudden additional impulse is given to the heeling of the vessel,
and she will take an extraordinary, and what seamen have often
called an unaccountable, lurch. Such a condition of waves and
ship reaching their greatest angle of inclination at the same
moment at regular intervals, is termed synchronising^ or in other
words, keeping time, and the effect is to produce considerably
greater angles of inclination in the ship than the steepest wave-
slope. The worst case is that where the period of a ship's single
roll is half that of the wave period, as
under such circumstances the impulse is
given on each wave, and. excessive rolling
is naturally set up. This can be further
illustrated by a simple pendulum (fig.
101).
Let us imagine that the pendulum has
just swung out to almost its greatest
angle of inclination in the direction of
the arrow. Suppose it receive a sudden ^^^ loi.— Influence of
impulse on the side B, it will naturally External Foeces on a
be checked, and commence its return to Swinging Pendulum.
the vertical position. But suppose, on
the other hand, the impulse had been given on the side A, at
the moment the pendulum reaches its greatest angle, when there
is neither return nor outward motion. The result is that a slight
impulse will considerably increase the extent of its outward move-
ment, and produce a greater angle from the vertical. This is
160 KNOW YOUR OWN SHIP.
exactly what happens with a vessel whose period of roll synchron-
ises with the wave period ; if a sudden impulse be given near the
extremity of her outward motion, a considerable augmenting of
the angle of heel will result. The eflfect is bad enough when the
synchronism occurs periodically — that is, with a series of waves —
but when it happens on every oscillation, the eflfect is still more
excessive, and the motion experienced by the vessel is rapid and
jerky, with the greater probability of producing dangerous results.
Stiff vessels with quick periods of about four to six seconds, would
be the most likely to develop such behaviour. Vessels of longer
or shorter periods may destroy synchronism altogether in most
cases.
Were all sea waves of the same length, period, and height, it
would be quite possible to design a warship or a yacht, whose
equipped conditions are of an unvarying nature, to give a
rolling period in still water which would produce great steadiness
among waves.
But sea waves, at different times and places, vary greatly in
length, period, height, and character. Atlantic storm waves
reach 500 feet and over in length from crest to crest, with
periods of 9, 10, or 11 seconds, and heights of 28 feet and over,
while in other localities the length may not be more than 200 or
300 feet, with varying periods of 6 to 8 seconds, and height of
about 12 feet.
Effect of Loading on Behaviour. — As waves, therefore, vary,
according to the locality, the force of the wind, etc., it must be
fairly clear that to design either a warship or a yacht to behave
always in the same manner among waves is impossible, for
although it is not likely that vessels with long rolling periods
will be -subject to heavy rolling, yet it is most probable that at
some time they may fall in with waves which synchronise with
their own period, and this inevitably produces heavy rolling.
With merchant steamers the difficulty in producing steadiness is
more marked than in any other case. In the first place, there
is the difficulty, especially in coasting vessels, whose loading has
to be rapidly conducted, with possibly part of the cargo arriving
just before they sail, of obtaining a certain metacentric height
which is known to have produced steadiness on a former occasion ;
or, if the metacentric height is the same, considerable difference
may have taken place in the positions of the weights of the cargo,
not vertically, but out on each side from the centre line of the
ship.
This brings us to another very important point. While small
metacentric height conduces to steadiness, the error must not be
fallen into that this mode of procedure can always be carried out.
ROLLING. 161
So long as the levers of stability at considerable angles be good,
and the range satisfactory, such a method is all very welL But
in tender vessels with short levers and short range, as seen by
curves Nos. 11, 12, 6, and 7, fig. 87, such a method is extremely
dangerous, for should synchronism be set up, they may take an
excessive roll and capsize altogether, so that it is evident some
vessels need more metacentric height than others, in order to
ensure safety, even though it produces more lively motions among
waves.*
Effect of Transverse Arrangement of "Weight on Rolling
Motion. — A safe method which can be adopted to assist in
producing steadiness in such a case, is to wing out the heavy
weights of the cargo, on each side of the vessel, without altering
their position vertically. Such an arrangement of cargo will
have a steadying effect upon lively transverse motions, and, on
the other hand, concentrating the weights in the middle line of
the vessel would tend to increase the rapidity of the transverse
rolling.!
Alteration in Behaviour during a Voyage. — In ocean
ships, whose loading is possibly not so hurried, or at any rate
the nature of whose cargo is often understood beforehand,
because it is all or nearly all alongside before commencing to
load, it is certainly possible to so carry out this method when
a knowledge of a ship's stability is understood, as to closely
approximate to a particular metacentric height, and moreover
to arrange the weights so as to be best fitted for steadiness.
Supposing we have secured a certain metacentric height which
has produced great steadiness even in a heavy sea, it is some-
times found that this same vessel in a long, low ground swell of
greater period, labours in a most extraordinary manner. Such
is not an unknown experience to seamen, and the cause is simply
due to the fact that the vessel has now fallen in with waves
which synchronize with her own period. An instance bearing
on this point was related to the author by a captain. Coming
from the Mediterranean with a light cargo, he encountered
heavy weather. His ship was naturally tender, and behaved
splendidly for some time, but on approaching the Bay of Biscay,
* It may here be Doted that it is utterly impossible to specify a meta-
centric height adapted to all vessels. For vessels in the Royal Navy, it
varies from 1 foot to 12 feet. In steam yachts 2'5 feet is probably an
average ; in sailing ships 2 to 4 feet is common, and in passenger and cargo
steamers it ranges from about 0*5 to about 3 feet. Shipbuilders with their
wide experience of the various types of vessels are undoubtedly most capable
of suggesting the best metacentric height for any particular condition of
loading. The foregoing metacentric heights are only for loaded conditions.
t See Appendix,
162 KNOW YOU^ OWN SHIP.
a long heavy swell set in, and the ship began to roll so heavily,
especially at periodic intervals, that he imagined she would
capsize altogether. He immediately set to work and filled one
of the water ballast tanks, with the result that the vessel com-
pletely altered in her behaviour, and again regained comparative
steadiness. The ship had evidently fallen in with waves which
synchronized with her own period, and caused the heavy rolling,
but by filling a ballast tank the metacentric height w^as increased
and the ship's period altered. Then, there being no longer
synchronism, she steadied. Every seaman naturally learns from
experience that where heavy rolling is suddenly set up, it can
be modified by an alteration in the course or the speed. The
reason is not far to seek. If the synchronism is produced by a
beam sea, by changing the course more towards the waves, the
apparent wave period is decreased, the crests being now passed
more rapidly. By taking a course in an oblique direction, away
from the direction at right angles to the waves, the wave period
is increased, and in any other sea than one direct abeam, an
increase in the speed without altering the course will decrease
the wave period. Thus synchronism can be prevented either by
altering the course or speed, and thereby altering the apparent
period of the waves, or by altering the period of the ship through
shifting weights in the ship.
Synchronism is not always produced by a beam sea, for the
sea coming in an oblique direction may cause the vessel's period
to synchronize with the wave period, when no such result would
have happened with a beam sea, and therefore such large angles
of roll could not have been experienced. How to obviate this
has just been mentioned — by changing the course or speed. To
attempt to alter the ship's period by filling the water ballast
tanks when rolling heavily is by no means a safe experiment, for
the moment of the free water dashing from side to side before
the tank is filled, may add to the angle of heel, instead of
reducing it. We must now be able to see that great stability is
not the best condition for a ship, for it will either make her
movements exceedingly rapid, following, as in the case of the
raft, the wave-slope, or, if not so stiffs, tending to produce
synchronism, with consequent heavy rolling.
The Metacentric Height. — The best vessel is undoubtedly
the one with moderate metacentric height, good levers of stahility
at considerable angles of inclination, and good range. She
will probably thus be slow in her period, easy in her move-
ments, and when not subject to synchronism (which she is less
likely to be) will be comparatively steady among waves.
To secure steadiness at the cost of small metacentric height,
ROLLING. 163
with short levers and range of stability, would only make disaster
more probable. This is the very reason why a ship's officer
should possess stability curves of his vessel in the various con-
ditions under which she is likely to proceed at sea, from which
he will undoubtedly be more able to intelligently manoeuvre the
condition of his ship in order to produce seaworthiness.
Could we imagine a vessel rolling among waves unresistedly
(that is, without being subject to resistance from wind, immersed
surface, or keel resistance of any sort), whose own period syn-
chronized with that of the waves, the effect would be that the
continued impulses given by the synchronizing waves would
eventually capsize her, whatever might be her stability, just as
a child's swing pushed synchronically would at last overset.
These resistances have the same effect among wave water as
when rolling in still water. There is one important point, how-
ever, to be observed, and that is, the more rapid the motions of
the vessel the more resistance is offered. And thus, upon a
vessel whose period synchronizes with the wave period, when
she begins to attain large angles of heel and great rapidity of
motion, the various resistances grow in proportion until a point
may be reached where the effect of these resistances is just
sufficient to prevent greater oscillation being attained, and cap-
sizing is also averted. Thus, where synchronism produces great
angles of oscillation, it does not follow that the ship will capsize,
except in unusual cases where the range of stability is very short.
The great and important value of bilge keels in offering resist-
ance and reducing rolling, has already been shown from Mr
Froude's experiments. These will produce good results upon
large ships, but the effect is still more apparent upon small
vessels of quick period.
Fore and Aft Motions. — Thus far our remarks have been
confined entirely to transverse stability and behaviour relatively
to transverse motions at sea, simply because that it is in these
directions that danger is most likely to occur. Could we heel
our ship in every possible way it would be found that she
possessed least stiffness or stability when inclined transversely
than in any other direction, and that her transverse metacentric
height is the smallest possible. Thus, on heeling in any skew
direction, more stability is developed, and most of all when
inclined longitudinally (pitching). In ordinary types of vessels
it is, therefore, only possible for them to capsize transversely,
unless it happens that, through damage and the admission of
water, the loss of buoyancy at either end is so great as to cause
the vessel to go down by head or stem, as the case may be.
This explains why it is only necessary to be- provided with
164 KNOW YOUR OWN SHIP.
curves of transverse stability, and to be thoroughly aware of the
vessels condition in this respect. The greatness of longitudinal
metacentric height will be obvious when it is observed that the
moment of inertia of the waterplane about a transverse axis must
be immensely increased beyond that for a longitudinal axis,
simply because what was formerly considered as beam in the
formula for the transverse metacentre becomes length, and the
length becomes beam.
The principles which govern transverse behaviour apply in a
similar manner when considering the longitudinal motions of a
ship, though here again the design may exercise much influence
in the production of objectionable qualities in behaviour. For
example, take an ill-designed vessel considerably full on the load
waterline aft, but fined away forward with sides almost vertical
to the gunwale. Such a vessel will be admirably adapted for
diving into the sea and shipping huge volumes of water on her
deck, with her stern probably high and dry. However, it must
not by any means be inferred that the load waterline forward
should be bluff* or even identical with the after end, but certainly
where any degree of comfort is desired, there should be some
reasonable approach to equality. A vessel, very fine under
water, may be considerably improved by giving her reasonable
flam * or flare above the waterline, the additional buoyancy pro-
duced by which forms a valuable check upon diving.
But we have also noticed that winging out the weights trans-
versely from the centre line produces slower rolling motion, that
concentrating them on the centre line creates greater liveliness,
and, moreover, that the latter result is always produced by a
large metacentric height, and steadiness by a moderate meta-
centric height.
Fore and Aft Arrangement of Weights. — With the enor-
mous longitudinal metacentric height — that is to say, length
metacentric height, not beam metacentric height — possessed by
most vessels, it is impossible to make any visible effect upon
the longitudinal motions through this agent, for even were it
possible to reduce or increase it by a few feet, the comparative
difference would be exceedingly slight. Moreover, such altera-
tion in the position of the centre of gravity might seriously
imperil the safety of the vessel transversely. Thus, the oaly
alternative is to influence longitudinal motion by a proper adjust-
ment of the heavy weights of the cargo in a fore and aft direction.
If liveliness is required — that is, quick rising motion — they should
* By flam is meant exactly the opposite to '* tumble home." It is most
noticeable at the bow of a ship, where her sides slant outwards, greatly
increasing her beam above the load waterline.
ROLLING. 165
be stowed nearest to midships ; if a slower movement is required
they should be spread out longitudinally (that is to say, more
fore and aft). But it must not be forgotten that placing heavy
weights at the extremities of a vessel has the tendency to exces-
sively strain the structure when subject to the varying support
of wave water, and also to some extent when lying at rest in
still water.
166 KNOW YOUR OWN SHIP.
CHAPTEK VI. (Section III.)
BALLASTING.
Contents. — Similar Metacentric Heights at Different Draughts — "Wind
Pressure— Amount and Arrangement of Ballast — Means to Prevent
Shifting of Ballast — Water Ballast — Trimming Tanks — Inadaptability
of Double Bottom Tanks alone to Provide an Efficient Means of Ballasting
— Considerations upon the Height of the Transverse Metacentre between
the Light and Load Draughts, and Effect upon Stability in Ballast —
Unmanageableness in Ballast — Minimum Draught in Ballast — ^Arrange-
ment of Ballast.
Ballasting. — The number of losses and disasters happening
annually, not only to old, but often to fine new ships when in
ballast, abundantly proves that something is wrong. This is
all the more manifest from the random way in which ballast is
often thrown into a ship. One man considers 400 tons sufficient,
and another, 800 tons for the same ship, and all pitched into the
hold. Both cannot be right, since both methods cannot produce
similar results. One is either dangerously stiff, conducing to
heavy rolling and tending to shift the ballast, or the other is too
tender with too small righting moments.
Before ballasting can be intelligently carried out, it is neces-
sary that a few important facts be kept in mind.
1. That metacentric height alone is no gitarantee for a vessel's
stability.
2. That freeboard alone is no safeguard.
3. That although a certain metacentric height on one occasion
may be very good for a vessel at a particular draught, the same
metacentric height would be unsafe at a different draught, and
even if it were possible to get the same lengths of righting levers
at a certain angle of inclination at light and load draughts, the
righting moments in each case would be immensely different.
Similar Metacentric Heights at Different Draughts. —
Reference to curves Nos. 5 and 18 (fig. 87) will considerably
help in illustrating these points. Curve 5 is for a box
vessel 100 feet long, 30 feet broad, 10 feet draught, and 5 feet
freeboard in the load condition, with a metacentric height of 6*2
feet, the centre of gravity being 6*3 feet from the bottom of the
box. Curve 18 is for a box vessel 100 feet long, 30 feet broad.
BALLASTING. 167
4 feet draught, and 16 feet freeboard in the light condition, with
a metacentric height of 6*2 feet, the centre of gravity being 14*5
feet from the bottom of the box.
Taking metacentric height and freeboard as the only guides,
the latter vessel should have by far the greatest stability.
A comparison of the curves contradicts such a conclusion, and
shows that the higher the centre of gravity is with a certain
metacentric height and freeboard, the smaller will the angle be
at which the vertical line through the centre of buoyancy inter-
sects the centre line of the ship below the centre of gravity, hence
the increased range of curve No. 5. Fig. 90 is the stability
curve for a sailing barque in the light condition, with 112 tons of
ballast aboard. The length is 270 feet, the breadth 41 feet, and
the freeboard 17 J feet, with a metacentric height of 2*9 feet and
a displacement of 1390 tons. The maximum lever of stability is
0*69 at 18° of inclination, and the righting moment 1390x0*69
= 959 foot-tons. Moreover, the stability vanishes altogether at
the comparatively small angle of 34°.
Wind Pressure. — Both the maximum lever and range are
exceedingly small for a heavily-rigged vessel with large sail area,
and the effect of a sudden squall of wind with much sail set is
easily perceived. In the loaded condition, however, with only 5J
feet freeboard, 4000 tons displacement, and a much lower centre
of gravity with the same metacentric height, this same vessel
would have longer levers and much greater moment, as well as
greater range of stability.
Amount and Arrangement of Ballast. — Now let us take a
practical view of the process of ballasting a ship, and suppose that
as master we are told by the naval architect or shipbuilder that a
metacentric height of 3 feet in the loaded condition, which gives
a displacement of 4000 tons, will put our ship in an excellently
seaworthy condition.
In the light condition, however, by placing 500 tons of ballast
in the hold, the same metacentric height is secured with a total
displacement of 2000 tons.
Heeled to an angle of 10°, the righting lever will be —
G M X sine of angle = 3 x 0*1736 = 0*52 foot.
As regards length of lever at this angle of inclination, the
vessels are practically identical at both these draughts. The
righting moment, however, is lever multiplied by displacement.
Thus, at the load draught the righting moment is 0*52 x 4000 =
2080 foot-tons ; at the light draught the righting moment is 0*52
X 2000= 1040 foot-tons — only one-half the loaded righting
moment. It is clear, then, that with equal sail area and equal
168 KNOW YOUR OWN SHIP.
wind pressure, the vessel in the light condition would heel to a
much greater angle than in the load condition ; moreover, the
effect of a sudden squall of wind will produce about double the
angle of inclination which would otherwise be reached in steady
heeling. There is always greatest motion at and near the surface
of wave water, so that the lighter the vessel, the more on the
surface she will float and be subject to the influence of waves and
wind. Possessing great stiffness under such conditions, the more
excessive wull be the rolling. Righting lever alone, then, does
not provide righting moment, but lever multiplied by displace-
ment. To get moment without excessive metacentric height,
there is no alternative but to considerably immerse the vessel in
order to get displacement.
Understanding this, we proceed to put ballast into our vessel.
Supposing the ballast to be sand, it would probably be found that
if it were all poured into the bottom of the hold, by the time
the ship was sufficiently immersed excessive stiffness would be
set up.
This method, therefore, cannot be adopted. We know that to
reduce metacentric height, low weights must be raised so as to
lessen the distance between the metacentre and the centre of
gravity. Part of the ballast, therefore, would require to be
carried in the 'tween decks. But here, again, a difficulty arises
in many cases, where a vessel with good beam, and a depth
to require two tiers of beams instead of having a laid deck on the
lower tier, this lower tier is made extra strong and the beams are
widely spaced, making it impossible to carry ballast higher than
the hold. What is to be done ? Very often nothing is done, and
only one or two conclusions can be arrived at, either the expense
of making provision for efficient ballasting is considered too much
for some owners whose vessels are amply covered by insurance, or
else out of pure ignorance of the mode of ballasting to ensure
safety, this subject receives no consideration. One thing which
could be done under such circumstances to produce excellent
results, would be to build two tanks at the middle of the length
of the vessel, one on each side, between the hold beams and upper
deck beams, to contain, say, about 50 tons each, or, altogether,
100 tons. JEach tank w^ould, therefore, require to be about 30 feet
long, 8J feet broad, and 7 feet deep. Especially if the ship were
fitted with water ballast tanks in the bottom, the size of these
upper tanks could be fixed to a nicety; but in any case, the
shipbuilder could supply the information as to the exact amount
of hold ballast to be used.
This would reduce the stiffness by raising the centre of gravity,
but furthermore, having these weights " winged " out to the ship's
BALLASTING. 169
sides, would still more conduce to steadiness. The application is,
therefore, twofold.
This method entails the expense of the plating, additional
beams, and pillars for supporting the tanks. Expense is always
objectionable, but there is the choice between possible and prob-
able loss of life through ignorance or carelessness in ballasting,
not to mention the ship ; and the comparatively small additional
cost upon the vessel while building. When loading cargo, and
these ballast tanks are not required, the space could conveniently
be used for cargo also, if a hatch be made on the deck above them.
The same idea could be carried out by constructing these
ballast spaces of wood battens, instead of iron plating, and using
earth or sand ballast. The former method is, however, preferable,
and economical, since the water could be run out by means of a
cock on the ship's side.
Means to Prevent Shifting of Ballast. — The other great
point in ballasting ships is to see that the ballast is secured so as
to render the likelihood of disaster from shifting impossible. If
it be water ballast confined in a tank, it is all right if the tanks
are full, for it must be remembered, as will be pointed out in the
remarks upon " water in the interior of a vessel," free water may
create a list if the vessel is inclined to be tender. But supposing
the ballast to be sand in the hold, great pre'caution should be
taken to make it immovable as far as possible. The value of
shifting boards as applied to cargo applies equally to this also, for,
after all, ballasting is just a form of loading.
Another method sometimes adopted is to cover the surface of
the ballast with boards and shore them down. This is all w^ell
enough if the covering and shoring is thoroughly carried out,
rendering no possibility of any ballast shifting, or finding its way
between the boards or uncovered spaces, for where such is possible
the precaution is useless, as the ballast will all the more readily
and easily relieve itself from its confinement.
Water Ballast. — Among a host of important considerations in
designing a vessel, draught is one which ever demands careful
attention. Limitations upon the depths of dock entrances,
harbours, rivers, etc., have in turn fixed the limits of depth and
draught for vessels. And thus, in many cases, while owners have
vastly increased the size of their vessels to carry a greater dead-
weight, the length and breadth almost entirely have furnished the
additional capacity, little alteration having taken place in the depth.
While earth, sand, or stone possesses certain advantages as
agents in ballasting, the cost entailed in loading and discharging
hundreds of tons of these materials often causes both serious loss
of time and expense. The advantage they possess is that they
170 KNOW YOUR OWN SHIP.
can be laid wherever desired in order to secure a certain condition
of ballasting — on the deck, in the 'tween decks, or in the hold
with perhaps, in some cases, precautions to prevent shifting as
previously pointed out. But with the adoption of iron for the
construction of ships, it was found that the bottom of the vessel
could be constructed so that while providing adequate and ample
strength, it might form at the same time a most convenient and
economical means of carrying water for ballast, for trimming
purposes, and for adjusting the stability under certain conditions,
not to mention the further important advantage of providing an
inner bottom, which has proved the salvation of many a ship,
when, by some means or other, the outer bottom has been so
damaged as to admit water. No doubt the division of this water-
tight space into separate watertight compartments gave to them
the more correct name of Trimming Tanks. For this purpose
they are admirably adapted, and may be fitted into almost any
type of cargo or passenger vessel with decided advantage. But
when these trimming tanks are used apparently with the expecta-
tion that they will also serve as an efficient means of ballasting,
one hesitates before calling them a universal success.
In these days of fluctuating freights, many vessels, especially
of the tramp class, find themselves without cargoes. To proceed
to sea with an empty tramp would be to court disaster. As
seamen know from experience, the enormous freeboard, slight
immersion, and sometimes deficient stability, would make these
vessels both extremely dangerous and utterly unmanageable in
bad weather. Ballast, therefore, becomes an absolute necessity.
And the tempting convenience of double bottom tanks has caused
them to be so widely adopted that their primary use has come to
be for ballasting purposes. A variety of forms of double bottom
ballast tanks have been built, but the system now generally
adopted is that known as the cellular double bottom. See fig. 55.
Inadaptability of Double Bottom Tanks to Provide an
Efficient Means of Ballasting. — And yet after we have got
this apparently commendable system of ballasting fitted into the
modern tramp, to whose lot it oftenest falls to do long, and even
Atlantic runs, in ballast, together with possibly a few hundred
tons of coal in bunkers, officers on board many of these vessels
complain of the miserable existence they endure in bad weather,
owing to the heavy rolling, disregard of helm, and general un-
manageableness of their ships. Something must be wrong some-
where, and as this double bottom tank does not produce the
results required, we had better examine the basis upon which it
finds its way into a ship.
Taking the specification of an ordinary cargo vessel which has
BALLASTING. 171
to be built to Class 100 Al at Lloyd's, we are pretty sure in most
cases to find the phrase " cellular double bottom all fore and aft
for water ballast to Lloyd's requirements." But what does
"Lloyd's requirements" mean? Kequirements for ballasting?
No. Ballasting lies entirely outside their province. Neither
Lloyd's nor any other of the societies for the registry and classifi-
cation of vessels, have any requirements for ballasting. Ballasting
is a feature in the ship design, and the owner, or whomsoever he
appoints to design his vessel, is solely responsible for the ballast-
ing arrangements. The owner may have practically whatever
design of vessel he likes, with whatever arrangement for ballasting
he chooses, such as, cellular double bottoms extending fore and
aft, or, through part of the length ; deep tanks ; peak tanks ;
hold, or part of hold spaces ; bunker spaces, etc. ; providing that,
so long as his vessel is built to the standards of strength fixed by
these societies, and the spaces intended for the carriage of water
as ballast are structurally to their satisfaction, the vessel will be
classed with a minimum freeboard.
A vessel may be built without any arrangement whatever for
ballasting purposes, and owing to her particular mode of con-
struction, it might be absolutely impossible to carry water as
ballast, yet she may still be perfectly eligible for the highest
class, and fully satisfy the requirements of the Board of Trade.
And when a double bottom system of construction is adopted,
it is never asserted that such space is adequate and properly
adjusted for the efficient ballasting of a ship, but it is simply
offered as a means of carrying water for ballast or for trimming
purposes, or for fresh water for the boilers, or for whatever
purpose owners may find it useful.
It would have been unnecessary to go into this detail were it
not for the fact that it is evidently very often and absurdly
assumed that because the double bottom is built to Lloyd's
requirements, the arrangement for ballasting is both proper and
sufficient. This is proved by the fact that large numbers of
vessels are constantly proceeding to sea dependent only upon
this ballast, together with a greater or less amount of bunker
coal on board. We have only to observe the method followed
in, say, Lloyd's rules, for arriving at the dimensions of cellular
double-bottom ballast tanks, to see that such could never be
intended as a competent mode of ballasting the various types
and differently proportioned cargo vessels.
Let us take an ordinary flush deck type of tramp steamer with
poop, bridge, and forecastle, built of steel to the three-deck rule,
and Classed 100 Al at Lloyd's. The dimensions are : length,
350 ft. ; breadth, mid., 45 ft. ; depth, mid., 29 ft.
172 KNOW YOUR OWN SHIP.
In order to find the particulars for the construction of the
ballast tank, we are instructed in Lloyd's rules to proceed as
follows : —
Find the 2nd numeral for scantling, as described on page 63.
For this vessel it is 32,506. Turning to Lloyd's rules we find in
a table relating to double bottoms a graduated list of similar
numerals. Tracing down this table, we arrive at the particulars
for tanks for vessels whose numerals are between 28,000 and
33,000. Here we see that the depth of the centre girder is 3' 6",
and the minimum breadth of the tank side is 2' 4".
The depth of the centre girder, or centre keelson, being de-
termined — which, by tlie way, is one of the most important items
in the structural strength of the bottom of the ship, since it regu-
lates the depth of the floors, and, to a large extent, the other side
girders in the tank also — the plating for the inner bottom is laid
over the top of these, and riveted, caulked, and made watertight.
And thus we have our ballast tank to Lloyd's requirements.
In fig. 102, curve 1 is for a modem beamy cargo vessel and
curve 2 for a vessel of the older and narrower type.
We observe, that at light draughts the metacentre is at the
greatest heights above the keel, simply because the extreme
fulness of the bottom of especially the beamy class of vessels
causes them to float at comparatively very light draughts with
very large moment of inertia of the waterplane in comparison with
the displacement at the same draught. It is found, however, that
by increasing the displacement the metacentre rapidly lowers, the
explanation being that the successive waterplanes above the light
draught increase very slightly in fulness, and consequently the
moment of inertia also is only slightly increased. The displace-
ment, on the other hand, increases much more rapidly in propor-
tion, and thus : —
Sliffhtly increased Moment of Inertia ,
— 2 — I = a very much
Greatly increased displacement in cubic feet
lower metacentre, notwithstanding the fact that with every increase
in draught, the centre of buoyancy has risen, and tended to keep
up the metacentre.
The downward tendency of the metacentre continues until, as
the vessel approaches her load draught, the ratio between the
moment of inertia of the lower waterplanes and the displacement,
and the moment of inertia and the displacement at the upper
waterplanes, has so altered, that the steady rising of the centre of
buoyancy has at last the effect of causing the metacentre to take
an upw^ard course again {see curves 1 and 2). Here, then, in
these natural movements of the metacentre it seems we have th^
secret of correct ballasting.
173
With the deductions and inferences we have made from these
simple considerations of the naetacenlre, we shall now revert to
our cellular double-hot torn tanks, and examine the complaints
lodfjed against vessels ballasted by means of them only.
First, then, mauy of them are heavy rollers, and cause estreme
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No. 1 Steamer, 360' x i7' Mid. x 28' Mid. Light draught, S' 6'.
Metacentre, 25' S" above keel.
No. 2 Steamer, 376' x 13' Mid. x 29' 1° Mid. Light draught, 12' 11".
Metoceotre, IS' 7}" above keel.
Fia. 102. — Curves of TniNsVEHSK Mbtacentbeb.
discomfort to those on board, in addition to severe straining to the
vessels themselves. Some of the narrower types of cargo vesacla
(notaljly older ones), have extremely little metacentric height, and
in some cases actually a negative metacentric height in the light
condition. (Compare heights of metacentre in light condition,
No8. 1 and 2, tig. 102.) By fiUing the double-bottom ballast
KNOW TOUR OWN SHIP.
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BALLASTING. 175
tanks, a decidedly positive metacentric height is obtained, which
possibly is not excessive, and these vessels are known as steadier
and better behaved at sea. But in recent years, considerable
additions, amounting to 2, 3, 4 feet, and more, have been made
to the beams of vessels with the corresponding increase in the pro-
portion of beam to depth and draught. The result is, that
though in both narrow and beamy vessels the centre of gravity
may be at the same height above the keel, the metacentre of the
broad vessel will be higher, and the metacentric height will be
greater, and some of these vessels are actually stiff and stand up-
right in perfect safety in a light condition. When proceeding to
sea light, the ballast tanks are filled ; the centre of gravity is thus
considerably lowered, and the naturally large metacentric height
is slightly, if at all, diminished. It will be remembered that the
metacentre lowers with increasing draught more rapidly than in
narrower vessels. Fig. 102 illustrates such a comparison. Many
of these modem beamy vessels are abnormally stiff, and as a
result earn the reputation of being unmistakably lively.
These remarks upon the metacentre may be further illustrated
by referring to fig. 103. Here we have a number of curves of
stability showing righting arms up to 90° of inclination.
Curve 1 is for a steamer, 376' x 43' x 29' 1", floating empty with
'78 of a foot metacentric height. This may be taken as a fair
representative of the narrower type, the proportion of depth to
breadth being '677. Unfortunately, we have no curve showing the
stability of the vessel in ballast. Eut probably with ballast tanks
and bunkers full, she would have approximately 2' 6" metacentric
height which, judging by the curve for the light condition, would
provide ample righting moment at large angles of inclination.
With this curve compare No. 2, which is for a vessel 302' x 40' 6"
X 24' 11". Here the proportion of depth to breadth is 'GIS, and
the metacentric height 7*3 feet emptyj and also compare No. 3,
which is for a vessel 360' x 48' x 27' 3". The proportion of depth
to breadth is '568, and the metacentric height 11*09 feet, empty.
The curves for these two vessels are fair representatives of a large
number of the more modem beamy cargo vessels. With ballast
tanks and bunkers full these two latter vessels have 5*63 and 8*45
feet metacentric height respectively {see curves 4 and 5), and with
bunker coal consumed and ballast tanks full, 7*15 and 10*83 feet
metacentric height respectively. {See curves 6 and 7.) It is
scarcely necessary to say that such metacentric heights as these
indicate enormous stiffness, the effect of which quality is well
known to seamen. As already stated, 7*3 feet is the metacentric
height for the 302 feet vessel light, and yet after the double-
bottom ballast tanks have been filled, and this large weight placed
176 KNOW YOUR OWN SHIP.
in the lowest possible position, the metacentric height is 7*15 feet,
actually less than for the light condition.
It is evident then, that, though the centre of gravity must have
lowered considerably, the metacentre has lowered a still greater
distance. With both ballast tanks and bunkers full, the metacentric
height is only 5*63 feet, owing probably to the fact that, the
bunkers being situated considerably higher than the water ballast,
the centre of gravity has not lowered very much, if at all, while
the metacentre, within these limits of draught, continues to
descend very rapidly for beamy vessels. These remarks apply
also to the 360 feet vessel, and an examination of the metacentric
heights for corresponding conditions will show similar results.
A much more marked difference is found in dealing in like
manner with the 376 feet vessel. To begin with, the metacentre
is within a foot or so of its lowest position at the light draught
(see curve 2, fig. 102), and the filling of ballast tanks could
not fail to lower the centre of gravity to such an extent as to
produce a greater metacentric height. As already approximated,
the metacentric height would be about 2*5 feet, and the curve
of stability would rise much more steeply and produce longer
righting arms.
We may also notice here that though the metacentric heights
and freeboards of both the 302 and the 360 feet vessels are
reduced by the filling of ballast tanks and bunkers, yet, owing to
the lowered centre of gravity, the righting arms are less for small
angles of inclination, as indicated by the reduced metacentric
height, and greater at larger angles of inclination.
Another complaint, especially against tramps in ordinary ballast,
is that of unmanageableness. No one would doubt the validity of
such an accusation against a ship sent to sea light without ballast.
But when properly ballasted surely a better state of affairs ought
to exist. As an example upon which to work, let us take a cargo
steamer whose deadweight capacity is 5800 tons. When fuUy
loaded, the freeboard is 5 feet. The cellular double bottom tank
has capacity for 900 tons of water, which is only about one-sixth
of the total deadweight. To this, say, 300 tons of coal are put on
board for bunker use. This gives a total of 1200 tons of dead-
weight on board in ballast sea-going condition, one-fifth of the
maximum deadweight. The draught is now 11' 6" on even keel,
against 23' 0" in loaded condition, and the freeboard is 16' 6"
against 5' 0". The propeller is slightly more than one-half
immersed in still water against more than total immersion w^hen at
load draught. Assuming her to be an ordinary full type cargo
vessel with a 10-knot speed and considerable stiffness in ballast,
she both rolls and pitches. The propeller in the best condition is
BALLASTING. 177
only partly immersed, and during her lively movements is subject
to intervals of immersion and emersion. In her pitching movements,
her often massive box-shaped fore end lends little assistance in
making headway, but is continually thumping against walls of water,
and the vessel actually experiences greater head resistance com-
paratively than she does in the fully loaded condition. There is,
moreover, less expenditure of propeller power in actually driving
her. There is the sudden shock produced by the propeller blades
striking the water after racing in mid-air, which is no doubt the
cause of what has become quite a frequent occurrence, viz., the
loss of propellers and the breaking of shafts. The rudder also adds
its decreased efficiency through decreased speed and periods of
emersion. Moreover, the huge freeboard, together with all
erections — poops, bridges, forecastles, deckhouses, etc., — exposed
to the force of a gale, with little or no keel resistance where a flat
plate keel is used, introduces more or less leeway into the category
of grievances, and where, as in some cases, the speed has become
an unknown quantity, actual drifting is a consequent result. To
reduce part of these ill features, after peak tanks have been fitted
in many vessels. By this means both propeller and rudder are
kept at greater immersion, but while the mean draught may
have been increased an inch or two, the fore end of the vessel has
suffered in emersion, and in attempting to steam with the wind
abeam, the effect in causing the vesseFs head to fall off will be
obvious.
Every seaman knows that the cure for excessive stiffness (large
metacentric height) is to raise weight already on board, or add
top weight, and thus raise the centre of gravity. Suppose the
first of these methods to be adopted. Instead of having a cellu
lar double-bottom tank throughout the length, let it only extend
over part of the bottom, and let the difference of the weight be
placed, say, in a part of the 'tween decks arranged for water
ballast. By such means we can arrive at practically whatever
metacentric height w^e desire. But this is sometimes rather a
dangerous experiment to make, and, as already pointed out, more
especially so in sailing-ships, for in securing what may appear a
desirable metacentric height we may rob our vessel of stability
most seriously, when she heels to considerable angles of inclination.
Going back to our curve of metacentres, No. 1, fig. 102, we
observed that the metacentre is very high at light draughts. To
attempt to approach such heights of metacentre with the centre of
gravity by raising ballast in order to make the ship easy, would
only increase the possibility of disaster. Every upward movement
of the centre of gravity shortens both the lengths of the righting
arms and the extent of the range of stability. So that by the
M
178 KNOW YOUR OWN SHIP.
time we have so raised the ballast as to produce a moderate and
desirable metacentric height, it is possible that the result is an
unseaworthy ship, that is, a ship with a good metacentric height
under other conditions, but with too little reserve stability at
possible angles of inclination. For be it remembered that most
carefully designed vessels may at times fall in with such a con-
dition of sea as to produce lurching to considerable angles of
inclination. It will easily be seen, then, how dangerous it might
be in the case of a beamy ship, if small metacentric height were
procured at the cost of decreased range and righting arms (fig. 104).
It is therefore evident, particularly in the case of beamy ships
floating at light draughts, with the usual amount of water ballast,
that there is no choice, in order to ensure safety, but to accept
larger metacentric height than required at load draught, which,
moreover, cannot be averted by the ordinary double-bottom ballast
arrangement, and in a spirit of resignation to put up with the rolling
and other accompanying consequences.
To produce safe and desirable results more ballast than is pro-
vided by the usual double bottom is required, not necessarily to
either raise or lower the centre of gravity to any great extent, if
at all, but rather to further immerse the vessel. Why ? Simply
because, as we have previously seen, by increasing the displace-
ment, the metacentre rapidly lowers, and by this manipulation of
the metacentre, we are relieved from indulging in any dangerous
experiment of raising the centre of gravity to a height such as
might produce disastrous results under the effect of heavy rolling
or lurching.
By placing more ballast on board (increasing displacement), a
safe compromise is effected between the metacentre and the centre
of gravity. Moderate metacentric height with the centre of
gravity in the lowest possible position will give the best results,
for by this means a slow and easy rolling period may be obtained,
combined with ample righting moment at large angles of inclina-
tion and sufficient range. This desirable condition could never be
attained by the usual method of only building tanks ^long the
bottom, varying from 3 to 4 feet in depth, as per Lloyd's rules.
Nor yet could it be accomplished if these tanks were increased to
twice their depth, which on no account could be advisable. For
though the more than doubled quantity of ballast would have
the effect of increasing the draught and the displacement, and thus
inevitably bringing down the metacentre, no compromise has been
made on the part of the centre of gravity, it having receded into a
lower position.
That more ballast is required to make both behaviour and
manageableness more satisfactory features many owners are
BALLASIIHG.
180 KNOW TOUR OWN SHIP.
perfectly aware, and in their specifications for new vessels they
have stipulated that deep tanks of some sort should he fitted in
some particular position in their ships. But even these have
not in all cases given such results as were expected. It has been
stated by some of those who have adopted them that the ships
behaved little better, and the tanks were often a source of trouble,
on account of leakage.
There is nothing very astounding in the fact that many ships
behave little better with such arrangement, simply because it is
fitted on much the same principle as the average stevedore loads
a ship he knows little about. In some cases these ships are almost
as stiff as when depending only upon double-bottom ballast, and
their behaviour at sea shows little, if any, improvement.
The trouble of leakage has very often been proved to be the
outcome of pure carelessness or ignorance. Instead of the tanks
being filled to the uttermost, empty spaces have been left at the
top, and, with a rolling ship, it does not require a very large
endowment of common sense to foresee what would happen with
so large a quantity of free water. An argument against these
tanks has been brought forward to the effect that it is difl&cult to
keep them thoroughly watertight, owing to the numerous severe
strains borne by a ship in ' her rolling and pitching movements.
A similar argument might apply to fore and after peak tanks, in
which localities very severe strains are experienced, and yet these
tanks can be kept watertight. Where outrageous proportions of
depth and breadth to length are adopted, such working might be
experienced as to make watertightness a doubtful quality, but in
the ordinary type of cargo vessel, with sound workmanship and
proper strengthening, there ought to be no special difficulty.
Minimum Seagoing Draught. — The important questions
then are. How much water ballast should be carried, and where
should it be placed ? As previously stated, it is desirable to get the
centre of gravity into the lowest possible position compatible with
a moderate metacentric height. Ketuming again to the curves
of metacentres, fig. 102, No. 1, for the beamy ship, shows that
the metacentre is over 25 feet above the keel at light draught.
With increasing draught it lowers, until, at about 18 feet draught,
it reaches its lowest position. Here, then, is probably the ideal
draught at which to fix the metacentric height. At no other
draught could tenderness — small metacentric height — be obtained
with greater safety with its accompanying easy rolling motion than
at this draught.
The centre of gravity is in the lowest possible position for such
a condition with ample freeboard, 5 feet more than at load
draught. The curve of stability would rise gently at firsts and at
BALLASTING.
181
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182
KNOW tOtJft OWN SHll*.
90'
Scale of Degrees.
Curves of stability for a steamer. Length, 302 feet ; beam, 40 feet 6 inches ; depth
mid., 24 feet 11 inches. Load displacement, 5183 tons. Freeboard, loaded condition
F = 4 feet 10^ inches. Poop, bridge, and forecastle.
Ship Complete— Steam up.
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Bunker
Coal, Stores,
and Fresh
Water.
Water
Ballast.
Cargo.
Maximum Stability.
Height of
Metacentre
above Centre
of Gravity.
Degrees.
Righting
Lever.
out.
in.
out.
in.
out.
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at 48 cub. ft. per ton.
ditto.
Coal cargo at
45 cub. ft. per ton,
ditto.
45
46
58
57
53
50
55
52
Feet.
3-31
2-68
5-58
4-77
1-85
1-45
2-22
1-78
Feet.
7-30
4-92
7-16
5-63
2-16
1-99
2-62
2-43
Condition F loaded with Homogeneous Cajeloo.
Upright. 13^" IncUnation.
Deck edge
immersed.
50° Inclination. 93° Inclination.
Maximum Vanishing
stability.
point.
Fig. 106.— Curves of Stability for a Steamer in Various
Conditions of Ballasting and Loading,
BALLASTING.
183
oor
SoALE OF Degrees.
Curves of stability for a steamer. Length, 360 feet ; beam, 48 feet ; depth mid.,
27 feet 3 inches. Load displacement, 8050 tons. Freeboard, loaded condition F = 5 feet
5 inches. Poop, bridge, and forecastle.
Ship Complete — Steam up.
•
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Maximmn Stability.
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Coal. Stores.
Water
Height
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and Fresh
Ballast.
Cargo.
a
o
Water.
Degrees.
Righting
Lever.
Feet.
Feet.
A
out.
out.
nil.
35
3-96
11-09
B
in.
;i
))
39i
3-58
8-09
C
out.
in.
. )
45
5-79
10-83
D
in.
a
1 1
46
518
8-45
E
out.
out.
Homogeneous cargo
at 51 cub. ft. per ton.
39i
1-68
3-16
F
m.
> )
ditto.
37
1-31
3-12
G
out.
)i
Coal cargo at
45 cub. ft. per ton.
43
2-25
4-02
H
m.
M
ditto.
41
1-82
3-92
Condition F loaded with Homogeneous Caego.
-1-
Upright.
12° Inclination.
Deck edge
immersed.
37° Inclination.
Maximum
stability.
79° Inclination.
Vanishing
point.
Fig. 107.— Curves of Stability for a Steamer in Various
Conditions of Ballasting and Loading.
184 KNOW YOUR OWN SHIP.
large angles of inclination would show ample righting arms and
range, and the large displacement would produce large righting
moment. To reach this enviable condition, no less than 3700
tons of weight, including water ballast and bunker coal, would be
required in this vessel. Ordinary double bottom and peak tanks
provide 1000 tons towards this. The bunkers contain, say, 500
tons of coal, and we find that 2200 tons more are wanted, which
would require considerable provision, and entail additional outlay.
But as shown by fig. 103, vessels of this class have such
enormous reserve stabilijty at large angles of inclination that, in
order to obtain a good condition of stability, it is not necessary to
get the metacentre into the lowest position, but, as the metacentre
lowers much more slowly as the 18 feet draught is approached,
by arranging the ballast, the centre of gravity may be so situated
as to give moderate metacentric height at a less draught with
perfect safety. But we have manageableness to consider as well
as stability, and it is probable that in order to get a satisfactory
combination of both, the vessel should be immersed to approxi-
mately about half the difference between light and load draught,
which means about 2750 tons for this vessel. By way of
illustrating positions for water ballast, examples are given in fig.
105, though a little consideration will show that many modifica-
tions or other combinations might be adopted. Each vessel has a
cellular double bottom fore and aft. In all the four examples it has
been assumed that the vessels have at least three decks, or are of
such depth as to require three decks or an equivalent to three decks.
Modification would naturally be necessary in vessels of less depth.
Example 1 shows a deep tank at each end of the engine and
boiler space. Where the fore one is shown, a cross bunker in
many ships is located. When full of coal, the coal would naturally
serve as ballast. By the introduction of additional strength it
could be built to carry water as ballast when not occupied by coal.
One or both of these tanks might better give the condition required
by being made shorter and carried up higher.
Example 2 shows an arrangement where one or both spaces in
the lower 'tween decks could be constructed for ballast.
Example 3 is another case showing the ballast higher still. In
some vessels this method could be carried out with perfect safety,
and a desirable metacentric height could be obtained without sacri-
ficing, to any serious extent, the stability at considerable angles
of inclination. A further advantage of such an arrangement of
locating the ballast at the sides of the vessel is, that it assists in
producing slower and easier transverse movements without making
any draw upon the stability, such as always accompanies the
raising of the centre of gravity. This space again could be used
BALLASTING. 185
for bunkers, and would naturally need special support in the form
of strong beams, pillars, etc.
Example 4 shows a ballast tank situated at the fore end of the
boiler space.
This, again, is in a common position for the cross bunker, and
might be used for such purpose when sufl&cient coal is carried.
Fore and after peaks, when properly constructed, may also be
used for ballast. The disadvantage of large fore and after peak
tanks is that, owing to the fineness of the ends of the vessel, they
are almost unsupported, and act as hanging weights along a lever,
causing severe straining, which is more excessive in the light con-
dition than any other.
In the foregoing examples the midship ballast spaces should be so
constructed, with watertight hatches and doors, as to be thoroughly
adapted for cargo or bunker coal, and adjusted to suit trim.
Indeed, in designing such spaces for ballast, a foremost con-
sideration should be to see that they are not rendered useless for
the carriage of cargo when ballast is not necessary. Another
important consideration is to adopt, when possible, such spaces as
by their requirements, apart from ballast, approach nearest to the
requirements for carrying water as ballast — such as watertight
'tween decks, bunkers, hold spaces, etc. By this means consider-
able saving may be made in the course of construction.
It w^ould be absurd to propose the introduction of ballasting
arrangements such as have been mentioned for vessels on regular
routes, and always sure of cargo, but where there is the possibility
and probability of occasional, and sometimes frequent, runs in
ballast, it appears that the best sea-going conditions can only be
arrived at by some such process. Nor could any of the methods
illustrated be recommended before making a thorough investi-
gation of the particular ship under consideration.
It is true that large ballast tanks add somewhat to the cost and
weight of a ship, though, as previously shown by the adoption of
certain spaces, where the usual construction lends itself for such
purpose, both cost and weight are kept down.
However, by the reduction of overdue voyages, and less consump-
tion of bunker coal, together with the greater safety of the vessel,
and the often vastly improved conditions of existence for those on
board, it would seem that additional ballast to that provided by
the ordinary cellular double bottom, carried in tanks properly con-
structed and adjusted, can only be worthy of commendation.
Note. — Actually fitted water ballast tanks, showing methods of construction
and special strengthening, are given in the author's companion volume, Con-
struction and Maintenance of Steel Ships.
186 , KNOW YOtJtl OWN sum
CHAPTERVI. (Section IV.)
LOADING— HOMOGENEOUS CARGOES.
Contents. — Alteration to Curve of Stability owing to Change in Metacentric
Height—Stability of Self-Trimming Vessels — Turret — Trunk.
Loading. — All cargo-carrying vessels are not of the same type,
proportions, or form ; therefore, they cannot all be loaded alike.
Loading does not mean, as some would imagine, the art of
throwing into the smallest possible hold space the greatest
amount of cargo in the least time. This method might do all
very well, probably, for the loading of railway trucks, when the
freight is not of a more damageable nature than sand or rubbish,
but to adopt such a method in dealing with so sensitive an object
as a ship, simply betrays unwonted ignorance. Certain ships
lend themselves more than others to the production of objection-
able results, but in the majority of vessels built in these days,
the person in charge of the loading or ballasting is often more
blameworthy for the bad stability and behaviour of his ship at
sea than the ship herself. By the term had stability is not only
meant too short righting levers or too short range (this might
be called deficient stability), but also too much stability, with
too long righting arms for small angles of heel, which produces,
as observed in Section II., rapid movements, and probably exces-
sive rolling.
Suppose the shipbuilder supplies a captain with a curve of
stability for his ship in her loaded condition, with a certain
metacentric height. This, while perfectly safe, he also finds
produces easy motion and general steadiness at sea. As far
as it is possible, he observes and makes notes of the distribution
of weights in the hold, as regards their vertical and horizontal
position — that is, if the cargo be of a miscellaneous character, and
strives to obtain a similar condition on each succeeding voyage,
testing at times, when doubtful, the metacentric height in the
load condition, before sailing. Now suppose in going to a strange
ship he proceeds to adopt exactly the same methods of loading as
in the previous one, it is extremely unlikely that similar results
would be obtained, for at sea we should probably find her
LOAblitG HOMOGBNiotJS CARGOES. l8?
behaviour widely different, and on testing the metacentric height,
that she had either far too much, or else too little, or possibly
scarcely any at all ; the diflference in form, proportions, type, or
arrangement of. permanent weights being accountable for this
result.
Thus we see that efficient loading demands much more know-
ledge, intelligence, and wise discretion than one would at first
imagine. Mere rule-of-thumb methods can only produce uncer-
tainty in the majority of cases. A clear understanding must
exist as to what is the best condition of seaworthiness.
For all vessels identical in their proportions, in type, and in
internal arrangement, it would be an easy matter to fix upon a
freeboard and metacentric height such as would ensure the best
possible results at sea ; but the immense variety of vessels which
are continually being built renders this impossible. However,
the officer who superintends the loading is relieved from the
former of these responsibilities, as this is fixed either according
to the rules of the Board of Trade and Registration Societies, or
else by the designers, who in some cases prefer to give more free-
board than the rule minimum. Neither can the officer deter-
mine the best metacentric height. Here, again, he is dependent
upon the builders or naval architect, who, by calculation, experi-
ment, and varied experience, are in the best position to specify
the metacentric heights under various conditions likely to prove
most satisfactory. The responsibility which does rest with the
ship's officer is the obtaining of the required metacentric height,
without which the freeboard determined by the Board of Trade
Rules (a freeboard which is calculated on the necessary condi-
tions being fulfilled to provide the ship in a state of seaworthiness)
is by no means of itself a guarantee of safety. As some captains
would remind us, it is true that probably with the majority of
ships built no such information is provided, much less curves of
stability. The reason has been given many times before —
viz., that in most cases the ship's officer does not know how
to use them if he got them. But it would be unjust to blame
him for not understanding a subject about which so little attempt
has been made to provide the proper means of obtaining a know-
ledge of their meaning and use. In the past there has been even
a worse feature than this. Probably there are no shipbuilders
who have more endeavoured to supply information of this nature
than Messrs William Denny <fe Brothers, Dumbarton, and yet
their experience is the regrettable one, that only in some
cases has their information been used. The happy side, how-
ever, is that, when it has been used, most satisfactory results
have been obtained. Shipbuilders have not been much en.
188 KNOW tOUR OWN SHIP.
couraged in the past to go to the additional trouble, except in
special cases, of providing information upon stability. It is
hoped, however, that with the ever - increasing facilities of
education for persons in all occupations, the subject will no
longer be relegated to the remote position it has hitherto held,
especially among oflBcers of the mercantile marine.
The writer's experience in lecturing has proved that the
importance of all the points dealt with in this book is already
being more fully comprehended, and that seamen generally are
desirous of acquainting themselves with them. Undoubtedly,
when such information can be used, shipbuilders, as a rule, will
be only too ready to supply it, if it were for no other reason than
the return which ships' officers would be able to make, in giving
reliable information to the shipbuilder, which would greatly
assist in the development of vessels thoroughly adapted for their
special trades.
At this stage a few observations may possibly be made with
profit upon the loading of homogeneous cargoes. Although in
some respects less complicated than those of a miscellaneous
character, nevertheless their varying densities necessitate that
their varying effects upon the vessel's stability be understood.
Homogeneous Cargoes. — By a Jtomogeneons cargo is meant
one all of the same kind, such as a complete cargo of cotton, or
coal, or wool, or grain, or timber. All homogeneous cargoes
which exactly till the holds, and bring a vessel down to her load
waterline, have the same effect upon the levers of stability, and
produce the same amount and range in every case. This is self-
evident, since the centre of gravity of every such cargo must
occupy the same position, thereby producing in each case
identical levers of stability. As the total weight of each such
cargo as brings the vessel to the same load waterline must be
equal, it follows that the moment of stability, which equals the
displacement multiplied by the righting lever, must also be
identical ; the other conditions, metacentric height and free-
board, which are necessary in the production of similar stability,
remaining constant. But supposing that we have a homogeneous
cargo of the nature of timber, which necessitates a part of it
being placed on deck in order to sufficiently load the vessel to
bring her down to the load waterline, then we alter the previous
conditions, and the stability is affected.
Having placed a part of the weight constituting the cargo
upon the deck, it follows that the centre of gravity will have
risen b}^ the distance of the centre of gravity of the deck cargo
from the centre of gravity of the ship (when laden with a homo-
geneous cargo, which simply fills the holds alone and brings her
LOADING HOMOGENEOUS CAKGOES. 189
down to the load waterline), multiplied by the weight of deck
cargo, and divided by the total displacement. However,
although the metacentre always occupies the same position
when the vessel is at her load waterline, and the freeboard is
constant, yet the reduction in the metacentric height, due to
the deck timber raising the centre of gravity, will result in
decreased levers of stability, and, consequently, decreased
moment and range. But, again, a vessel laden with a light
homogeneous cargo, which, like timber, does not put the vessel
down to the load waterline when the holds are filled, and is of
such a nature that if exposed to the weather would suffer
damage, has, consequently, considerably more than the necessary
freeboard. The probable result in most cases would be a
reduced metacentric height. This would in all likelihood be
caused by a lowering of the metacentre and raising of the
centre of gravity. It is true that the metacentre ought, accord-
ing to the formula, to be at a greater height above the centre of
buoyancy, owing to the decreased displacement and very slightly
reduced moment of inertia of the new waterplane ; but then the
centre of buoyancy has lowered also, owing to the lesser draught,
which, altogether, may have produced in the region of the load
waterline a lowered metacentre (see Metacentric Curves, fig.
115). This, however, could readily be ascertained from the
curve of metacentres.
Coming to the centre of gravity, we should most likely find
that the centre of gravity of a homogeneous cargo filling the
holds lies below the centre of gravity of the vessel in her light
condition ; so that the loading of such cargo must produce a
centre of gravity for the loaded ship below the centre of gravity
in her light condition. When such is the case, it, moreover,
follows that the heavier the homogeneous cargo, the greater its
effect in producing the lowest centre of gravity and the greatest
metacentric height. The lightest homogeneous cargo would
therefore produce the highest centre of gravity and the least
metacentric height. Thus the conclusion should not be jumped
to that the greater freeboard will compensate for the loss of
metacentric height and raised centre of gravity, for it might
very possibly be found that the whole range of stability had
suffered reduction, which would be further influenced by the
smaller displacement.
On the other hand, with a homogeneous cargo which puts
the vessel down to her load waterline, and yet does not fill the
holds, it follows that the centre of gravity must occupy a lower
position than when laden with a homogeneous cargo filling the
holds. The result in this case is, that the metacentric height
190
KNOW YOUR OWN SHIP.
being greater and the freeboard unchanged, the lever of stability
is lengthened and the moment and range are increased ; so that
for a vessel engaged in general trade, the value to a shipmaster
of a curve indicating her stability when laden with a probable
light, homogeneous cargo, which causes her to draw considerably
less water than her load draught, and another, when laden with a
denser homogeneous cargo, exactly putting her down to the load
waterline, must be obvious.
To find Alteration to Curve of Stability owing to a
Change in Metacentric Height. — Having given the meta-
centric height and a curve of stability for a vessel at a certain
draught, it is a very simple matter to find the new curve of
stability when any change has taken place in the distribution of
Fig. 108.
the weights of the cargo in loading, and thereby altering the
metacentric height, as long as the same draught is maintained.
Fig. 108 shows a vessel floating originally at the waterline
W L, but under inclination at the waterline W L'. B is the
centre of buoyancy at the new waterline. G, G\ G^ are three
positions for the centre of gravity, produced by different arrange-
ments of miscellaneous cargo upon three successive voyages. Let
it be assumed that a curve of stability has been provided for the
first condition of loading. The distance from G to G^, and G^ to
G^, is, say, 1 foot. Under the first condition of loading, the right-
ing lever is G Z, under the second condition it is G^ Z, — that is,
G Z reduced by the part G k,
G A; = G G^ (1 ft.) X sine of the angle of inclination.
G Z - (G G^ X sine of angle of inclination) = G^ Z.
G Z - (G G^ X sine of angle of inclination) = G^ Z.
The new levers for the curve of stability for any condition of
loading are thus found by multiplying the distance the centre of
LOADING HOMOGBNBOUS CARGOES.
191
gravity has risen by the sine of the angle of inclination, and
deducting the result from the original levers of stability. Should
the centre of gravity have lowered, then the correction will re-
quire to be added to the levers of stability. (See fig. 104.)
This is both important and exceedingly useful to a ship's
officer. For example, his vessel's loaded seagoing draught is
fairly constant, and having once been supplied by the designer or
shipbuilder with the metacentric height, and a curve of stability
for the vessel loaded with a homogeneous cargo, he can always
readily ascertain what his curve of stability is for any other con-
dition of loading at the same draught. This is further important,
because the metacentric height for one vessel at the load draught
may be quite unsuited and even dangerous for another vessel at
her load draught. Many Atlantic liners have only a few inches
metacentric height, being purposely designed in this way in order
to make them easy and comfortable at sea. But there is no
danger of their capsizing through lack of stability, for as soon as
they begin to heel, their righting levers of stability begin to grow
Figs. 109, 110, and 111.
in length, owing to their great freeboard and true proportions.
(See figs. 92, 93, 94, 106, 107.)
In some measure this applies also to cargo vessels with
great freeboard, such as awning and spar-decked vessels. The
metacentric height in well-proportioned vessels of these classes,
when properly loaded, would be satisfactory at about 1^ feet.
Where excessive beam is adopted, it becomes almost impossible,
and also most dangerous, to attempt to follow the metacentre in
its high altitudes by using every possible means to raise the centre
of gravity. There is no alternative in such vessels but to put
up with their heavy rolling, lurching, straining, and general dis-
comfort.
Vessels with very low. freeboard necessarily require greater
metacentric height, and more especially so if, in addition, they are
very beamy. Naturally, great beam produces large metacentric
height, unless it is overruled in the process of loading.
Now, in designing a vessel, unless flill particulars are given of
the exact nature of the cargo to be carried, the designer works upon
192 KNOW YOUB OWN SHIP.
the assumption that the holds are exactly filled by a cargo of a
homogeneous nature. During recent years, a number of new types
of vessels have presented themselves, such as the " Turret,"
"Trunk," and "Self-trimming" types. (Figs. 109, 110, 111.)
There is no doubt that these vessels have certain advantages,
especially in the nature of their self-trimming capabilities. The
reserve buoyancy afforded by the turret, trunk, or other self-
trimming erection is rightly taken into account in .determining
the freeboard, and, as a result, the deck is brought much nearer
to the water level. But with the good beam which it is usual to
give to these vessels, ample metacentric height is provided, so
that, when loaded with a homogeneous cargo (the only way in
which to make a fair comparison of vessels), there is no doubt
that their designers and builders have amply provided for all
demands upon their stability that wind and weather are likely to
make.
8Hl^'J?IlJ(J CARGOElS. l93
CHAPTER VI. (Section V.)
SHIFTING CARGOES.
Contents. — Variations in Stability on a Voyage.
Shifting Cargoes. — Professor Elgar, in a most valuable and
instructive paper read before the Institute of Naval Architects,
in 1886, upon " Losses at Sea," states that in the three years,
1881, 1882, and 1883, out of 264 British and Colonial vessels
registered in the United Kingdom of and above 300 tons gross
register, which had been lost at sea under the category of
** foundered or missing," one-fourth of these were laden with coal,
and one-sixth with grain — ^very large percentages of the total
losses from these causes. It must be remembered, however, that
A.
c
^^^^^^w^"^^''
STAR
*
e
Q
BO
•
jE^
- ~ ^^'""""'''^
t
:^J^5£r>5^
p^
... _jr_ ZL**- ' /
y —
ffr — '" — ^"""7
Fig. 112. — Vessel with Cargo Shifted,
these are two of the largest trades in which British vessels are
engaged, but at the same time it is obvious that they are two of
the trades in which there is most possibility of cargo shifting.
Hence the precautions insisted upon by the Board of Trade in
the case of vessels carrying grain in bulk, that proper feeding
arrangements be adopted in order to keep the hold spaces filled ;
that proportions of grain to be carried in bags; and also that
shifting boards be fitted down the centre of the holds, extending
from keelson to deck, and in 'tween decks from deck to deck.
Without such precautions, where both grain and coal are carried
entirely loose in the hold, the danger is easily perceivable.
196 KNOW YOUR OWN SHIP.
Take an ordinary cargo vessel which on a six days' voyage
from one port to another consumes, say, 100 tons of . coal.
Naturally the displacement will be reduced by 100 tons, and
by referring to the " tons per inch " curve it may be ascertained
how many inches the draught has decreased, evidently giving
greater freeboard in the first place.
The effect upon the metacentric stability will depend chiefly
upon the position of the centre of gravity of the bunker coaL
In the case where the bunkers are situated on each side of the
boilers, and in a cross bunker extending from the top of the
floors to the first deck when there are two or more decks, the
centre of gravity of the bunker coal will generally lie below the
centre of gravity of the ship, making the ship stiffer. When
the coal is consumed the vessel will become more tender, and
usually steadier when among waves, due to the reduced meta-
centric height.
But as is more common in these days among tramp steamers
of good beam, where, in order to get the greatest reduction on
the tonnage by obtaining the largest possible propelling space
(see Tonnage), the practice of almost dispensing with lower side
and cross bunkers is adopted, and the coal is carried in the
'tween decks at the sides of the engine and boiler casings.
Frequently an additional 30 or 40 tons are placed on the bridge
deck, and kept there by means of temporary boards secured to
the rails, or by closed-iron bulwarks. In such cases the centre
of gravity of the coal is much above the centre of gravity of the
ship, producing reduced metacentric height and greater steadi-
ness. But on the consumption of this coal, the top weight
being removed, the centre of gravity lowers, the ship becomes
stiffer, and is found to roll more than previously.
After lecturing on this subject on a certain occasion recently,
a captain who was one of the audience related the following
uncommon incident in his own experience, an incident which he
had never been able to understand : —
Coming up the Irish Sea to Liverpool almost at the end of a
homeward voyage, laden both in holds and on deck with esparto
grass, the vessel began to indulge in most peculiar movements.
There was not much sea, and previous to this time the vessel
had been exceedingly steady ; but now she commenced to take
a slight list, and to move occasionally from side to side with a
jerk, and not with a rolling motion. She would then lie still
after one of these movements, except for the rising and falling
of the waves, until after another interval another wave lifted
her up, and she jerked to the other side, there again lying for a
time, the motion being repeated at intervals. As this captain
SHIFTING GARQOBS.
195
the hold is at as large an angle a^ the surface of the heaped
grain, before any shilt takes place. If the ship could be heeled
Blowly and steadily, no shift of cargo would occur before the
surface of the grain has reached aa great an angle as it is possible
to heap it upon a floor, as in fig. 113, ab and a & being at the
same angle of inclination.
If this answer were correct in all cases, possibly a littls less
uneasiness might be felt as regards shifting cargo, for the late
Professor Jenkins, in a paper read before the Institute of Naval
Architects, on this subject, gives the ■greatest angles to which
it is possible to heap a free surface of wheat (or, as it is termed,
the angle of repose) at 23J°, which is considerably less than that
of most grain, and as grain-laden vessels are generally inclined
to be tender, and, therefore, usually roll less, the angles of repose
Fio, 113.— Ahqle of Repose poa Graih.
for grain are greater than many such vessels would roll through.
But this is not the case, for the effect of rolling, pitching, and
blows from the sea is to reduce the angle of repose considerably.
Moreover, movement of cargo will take place aU the sooner, the
gi-oater the distance its surface is situated from the centre about
which the ship rolls ; hence, cargo in the 'tween decks will shift
sooner than cai^o in the hold.
"When it is known that shifting boards extending down the
middle line of a ship reduce the heeling moment of shifted cargo
to about one-fourth of what it would be without them, their
value will then bo better understood.
Variationa in Stability on a Voyage. — Steamers are
especiaUy liable to considerable change in their stability and
behaviour at sea between the time of leaving one port and
arriving at another.
This is chiefly due to 'the consumption of bunker coal.
196 KNOW YOUR OWN SHIP.
Take an ordinary cargo vessel which on a six days' voyage
from one port to another consumes, say, 100 tons of . coal.
Naturally the displacement will be reduced by 100 tons, and
by referring to the " tons per inch " curve it may be ascertained
how many inches the draught has decreased, evidently giving
greater freeboard in the first place.
The effect upon the metacentric stability will depend chiefly
upon the position of the centre of gravity of the bunker coal.
In the case where the bunkers are situated on each side of the
boilers, and in a cross bunker extending from the top of the
floors to the first deck when there are two or more decks, the
centre of gravity of the bunker coal will generally lie below the
centre of gravity of the ship, making the ship stiffer. When
the coal is consumed the vessel will become more tender, and
usually steadier when among waves, due to the reduced meta-
centric height.
But as is more common in these days among tramp steamers
of good beam, where, in order to get the greatest reduction on
the tonnage by obtaining the largest possible propelling space
(see Tonnage), the practice of almost dispensing with lower side
and cross bunkers is adopted, and the coal is carried in the
'tween decks at the sides of the engine and boiler casings.
Frequently an additional 30 or 40 tons are placed on the bridge
deck, and kept there by means of temporary boards secured to
the rails, or by closed-iron bulwarks. In such cases the centre
of gravity of the coal is much above the centre of gravity of the
ship, producing reduced metacentric height and greater steadi-
ness. But on the consumption of this coal, the top weight
being removed, the centre of gravity lowers, the ship becomes
stiffer, and is found to roll more than previously.
After lecturing on this subject on a certain occasion recently,
a captain who was one of the audience related the following
uncommon incident in his own experience, an incident which he
had never been able to understand : —
Coming up the Irish Sea to Liverpool almost at the end of a
homeward voyage, laden both in holds and on deck with esparto
grass, the vessel began to indulge in most peculiar movements.
There was not much sea, and previous to this time the vessel
had been exceedingly steady ; but now she commenced to take
a slight list, and to move occasionally from side to side with a
jerk, and not with a rolling motion. She would then lie still
after one of these movements, except for the rising and falling
of the waves, until after another interval another wave lifted
her up, and she jerked to the other side, there again lying for a
time, the motion being repeated at intervals. As this captain
SHIFTING CABG0B8. 197
now explained, the vessel having a light homogeneous cargo,
had been very tender, and all the more so with the deck cargo.
The bunkers being situated low down in the vessel, the con-
sumption of coal on the homeward voyage must undoubtedly
have still further reduced the metacentric height. Moreover,
during the latter part of the voyage the deck cargo became
soaked with rain, which made it heavier and more effective in
raising the centre of gravity, until at last the centre of gravity
actually coincided with or rose above the metacentre. In the
latter case an upsetting lever having arisen, the vessel heeled,
until by the immersion of a new wedge of buoyancy this heel-
ing force was absorbed. The vessel was now practically in a
similar condition to the homogeneous cylinder we considered in
tig. 98, except that on being still more inclined, the immersion
of another new wedge of buoyancy caused the righting levers of
stability to grow again, which resisted further inclination.
Thus the cause of the vessel jerking from side to side was not
due to the effect of any righting moment, but simply to the
heaving motion of the sea pushing her occasionally to the up-
right, and then losing her balance, being in a state of neutral
equilibrium, she dropped over to the other side.
Any vertical movement of weights, or increase or decrease of
weights already on board, will in some degree influence the
stability, which, as has been shown, will affect her motion among
the waves.
Emptying or filling water ballast tanks may have a similar
effect.
198
KNOW TOUR OWN SHIP.
CHAPTER VI. (Section VI.)
BPPBCT OP ADMISSION OP WATER INTO THE
INTERIOR OP A SHIP.
Contents. — Admission through a hole in the Skin into a Large Hold —
Curves, showing Variation in Height of Metacentre with Increase of
Draught — Buoyancy afforded by Cargo in Damaged Compartment —
Longitudinal Bulkheads — Entry of Water into Damaged Compartment
beneath a Watertight Flat— Entry of Water into Damaged Compart-
ment above a Watertight Flat — Value of Water Ports — Water on
Deck — Entrance of Water through a Deck Opening — Entry of Water
into an End Compartment — Height of Bulkheads — Waterlogged
Vessels.
Effect of the Admission of Water into the Interior of a
Ship. — 1. Through a hole in the Skin below the Load Water-
line : —
Let fig. 114 be a box-shaped vessel 100 feet long, 20 feet broad,
10 feet draught, and 5 feet freeboard. For the saJke of example.
-w
i.
~yN
fiS^
?*
i¥s^3
•
f = £^s
Fig. 114. — ^Effect of Entry of Water into a Central
Watertight Compartment.
let there be a watertight compartment, one-fourth of the length
of the vessel — viz., 25 feet -—situated at the middle of the length,
and bounded at each end by a watertight bulkhead, as shown.
We will suppose this compartment to be damaged by collision,
and the sea to enter by the hole indicated.
After the damage the draught of water will have increased
from W L to wl^ for, as was pointed out in the Chapter on
Buoyancy^ the buoyancy of the compartment into which the
water has entered having been lost, in order to support the
weight of the vessel which remains unchanged, the reserve
buoyancy in the other intact compartments has had to be drawn
upon, hence the increase of draught. But let us see what effect
EFFECT OF ADMISSION OF WATER INTO SHIFTS INTERIOR. 199
this has had upon the metacentric height. The rule for the
height of metacentre above centre of buoyancy is —
Moment of inertia of waterplane
Displacement in cubic feet
Now, in taking the moment of inertia of the new waterplane of
this vessel, the compartment into which the sea has entered is
entirely ignored, and treated as though it were no part of the
vessel, since it affords no buoyancy. The moment of inertia of
the new waterplane w Z, less the part F G, divided by the dis-
placement, gives the height of the metacentre above the centre of
buoyancy. It will be pretty evident that the moment of inertia
will have decreased considerably owing to the loss of a part of the
waterplane area, which must result in bringing the metacentre
nearer to the centre of buoyancy. The position of the centre of
gravity of the ship remaining unchanged, it would appear to
follow, at first sight, that in every such case the metacentric
height is reduced. But let not the important fact be overlooked
that the centre of buoyancy must have risen with the increase of
draught. Possibly a simple calculation may more effectively
throw further light upon this. Referring to the box vessel before
the accident occurred : —
The displacement was 100 x 20 x 10 = 20,000 cubic feet.
The moment of inertia of the waterplane = ^ ^ - 66666.
*^ 12
The metacentre above centre of buoyancy = — ~ = 3*3 feet.
^ ^ 20000
The metacentre above the bottom of the box is 5 + 3*3 = 8*3 feet.
Let the centre of gravity be, say, 6*3 feet from the bottom of the box,
then the metacentric height in the undamaged condition is 8*3 - 6*3 = 2 feet.
For curve of stability (see fig. 87, curve No. 3).
After the collision, the draught is found to have increased 3*3 feet; this
is arrived at by dividing the volume of the lost buoyancy F G B A (fig. 114)
by the total area of the waterplane, less the part F G.
The centre of buoyancy is therefore —
^^ '*' ^'^ = 6*6 feet from the bottom of the box.
2
The displacement remains unaltered at 20,000 cubic feet.
75 X 20^
The moment of inertia of the waterplane = - — = 50000.
*^ 12
The metacentre above the centre of buoyancy = = 2*5 feet,
^ ^ 20000
which is lower than formerly.
The metacentre above the bottom of the box = 6*6 + 2*5 = 9*1 feet,
which is higher than formerly.
Then the metacentric height after the collision is 9*1 - 6*3 = 2*8 feet,
which is greater than formerly.
200 KNOW YOUR OWN SHIP.
Thus we see that the vessel has actually a greater metacentrio
height after the accident with the compartment flooded than she
had originally in her intact condition. At first, one is almost
tempted to jump to the conclusion that this could scarcely be
the result, for if such be the case, why the loss of so many
vessels subdivided into numerous watertight compartments ? and
we may point to the battleship " Victoria," and the more recent
disaster to the "Elbe." To understand this, it is necessary to
carefully trace the effect of the chief influencing agents, upon
which the initial or metacentric stability depends, from the
moment the collision happens to its climax. Be it observed,
however, that while the metacentric stability is less for this
box ship in the undamaged condition, yet the stability for
greater angles of inclination is unquestionably superior. This
is accounted for by the greater freeboard. Moreover, all ships
cannot bo classed as boxes, and the difference in form and the
fining away of the waterlines (or beams) towards the ends, has a
very marked efl'ect upon the height of the metacentre, owing to
the great reduction in the moment of inertia of the waterlines.
Variation in Height of Transverse MetSrCentre owing to
Increase of Draught. — It is generally found in merchant
vessels that for light draughts the metacentre is highest, owing
to the small displacement in comparison with the moment of
inertia of the waterlines, but as the draughts increase the
immense bulk of the vessel grows more rapidly in proportion
than does the moment of inertia. The result often is that the
metacentre falls, until, when approaching the load waterline, the
lowering effect of the increasing displacement is less than the
raising effect of the centre of buoyancy, owing to the increasing
draught, and the metacentre rises again.* This leads us to the
important fact that dangerous as the shipping of heavy seas
may be into large wells upon the decks of many vessels, yet in
some cases, owing to the increased draught from such sudden
deck weight the metacentre rises, and this greatly tends to
avert what might often be a serious condition.
In fig. 115 several examples are given for different types of
actual ships, showing the effect of increased draught upon the
heiglit of the metacentre, as shown by the curves. The table
on the same page gives the particulars for each vessel.
It will also be noticed that a collision happening in way of a
moderately large compartment at or near amidships, the loss of
this most effective moment of inertia of waterplane (the beam
being greatest here), greatly modifies the results obtained from
* Flaro out on the load watorlino at the ends of a vessel increaBOS thQ
ni^oxDent of inertia and tends to produce the 8ai;ne results,
EFFECT OF ADMISSION OF WATER INTO SHIp's INTERIOR, 201
vessels of box form, and makes impossible such increase in meta-
centric height as is obtained from our box vessel with its central
compartment flooded (fig. 114). In the box vessel in our illus-
2^
zz '
2.0
a>
<u
M
JS -
«m
o
%
16 '
H
«i
>
o
M-
J=>
a
*a
4)
72-
««H
a
•^^
CO
4J
70'
fii
«fi
a>
A
9 ■
••-.
o
(i>
«
c •
z •
of Draughts in feet.
Fio. 115.— Curves of Metacentres, showing Upward Tendency
IN Region of Load Draught.
No. of
Vessel.
1
Leugth.
Breadth.
Depth
Moulded.
Load.
Draught.
Description.
Feet.
Ft in.
Ft. in.
Ft. in.
1
320
45 3
28
22
Full sailing ship.
2
270
41
26 3
21
Full sailing ship.
3
206
28 6
15 10
14
Fine steamer.
4
231
32
17 4
15
Moderately full steamer.
5
215
31 10
16 3
15
Moderately full steamer.
6
245
33
17 3
15 9
Moderately full steamer.
/
190
27 6
18
12
Steam yacht.
8
162
22
14 4
11 6
Steam yacht.
9
154
22
13 6
9
Steam yacht.
202
KNOW YOUR OWN SHIP.
tration the draught was 10 feet, and the freeboard 5 feet, and if
these figures be for loaded conditions, the amount of freeboard,
and, consequently, reserve buoyancy, is exceptionally great.
Had there been anything less than 3*3 feet freeboard she would
have foundered, the weight of the vessel more than swamping the
total remaining buoyancy after the collision. But probably neither
the ** Victoria " nor the " Elbe " sank from this cause, for before
the reserve buoyancy had been exhausted they capsized.
Let fig. 116 represent the section of a vessel in way of a
Fig. 116.— Influx of Water into Damaged Compartment.
damaged compartment, the buoyancy of which compartment is
less than the remaining reserve buoyancy, thus proving that
there is, at any rate, capacity to float after the inflow of water
has ceased.
Water flows in through the hole X, and if the hole be large,
Fig. 117. — List Caused by Influx of Water.
as it usually is under such circumstances, the immense weight
of water which rushes in on tJie one side^ together with the
natural tendency of water to find the lowest possible positioDp
has the effect, for the time being, of drawing out the centre of
gravity of the vessel in the same direction — that is, towa|r4B tb©
EFFECT OF ADMISSION OF WATER INTO SHIP's INTERIOR. 203
side of the ship where the hole is, and the vessel takes a list.
The water already in the compartment naturally seeks a hori-
zontal surface, as shown in fig. 117, with its centre of gravity g,
well over to the heeling side, adding to the inclination.
The continuous pouring in of water, accompanied by increasing
list, and the added effect of the water which has already entered,
combine to increase the heeling process, and thus eventually, in
many cases, when the heeling moment from these causes exceeds
the greatest righting moment indicated by the vessel's curve of
stability, she capsizes. If the vessel be very stiflf in the upright
condition, in some cases she will resist the heeling caused by the
water pouring in, and she will do this all the more easily after
a moderate quantity has entered, as this has the effect of lowering
the centre of gravity and adding to the stiffness and resistance
to further inclination, and eventually, when the reserve buoyancy
has been drawn upon for the loss of the buoyancy of the damaged
compartment, she may remain at rest in a condition of stable
equilibrium, unless the change of trim has been so great as to
cause the vessel to go down by the head or the stern
Buoyancy afforded by Cajrgo. — It should be noted that
immediately after the collision the weight of water pouring in
c o
Fig. 118. — Effect of Water in a Compartment with Cargo.
acts exactly as deadweight, lowering the centre of gravity and
increasing the draught. But after the compartment is filled to
the level of the water outside the ship — and the water inside the
ship continues to be freely in contact with the water outside —
the entered water is no longer considered as weight, any more
than the water outside the ship is weight, since this space has
ceased to represent floating power (excepting the cubic capacity
of the cargo inside, if there be any, for displacement is always
actual buoyancy), and the entered water is, therefore, dismissed
as being no part of the vessel ; in fact, the vessel is now identical
with fig. 118.
Here we have two intact end compartments. The middle
space, A B C D, has only, say, a bottom upon which rests weights
representing cargo. There are no sides to this compartment, but
simply the means for holding the structure together. In this
204 KNOW TOUR OWN SHIP.
example we have an exact illustration of the vessel we have been
considering. The whole is being supported by the buoyancy of
two intact end compartments, together with the volume of the
cargo, which also affords its cubic capacity of buoyancy, though
beneath the water level. The centre of gravity is the actual
centre of the weight of the ship and her cargo, the water in the
space over the cargo neither affecting its position nor adding to
the weight.
Thus we see that in an actual ship the entry of water may at
first affect the centre of gravitj'', yet after the inflow has ceased,
having reached the water level outside, the centre of gravity is
again in its original position. If the vessel is tender in the
upright condition, she will heel all the more easily under the
effect of water so entering.
Longitudinal Bulkheads. — Should the vessel possess a longi-
tudinal watertight bulkhead down the middle of her length,
instead of this providing a means of safety, as is sometimes sup-
posed in such an accident, it simply adds to the effect of the
water in heeling the ship, and by robbing the ship of buoyancy
upon one side only tends all the more to the proiiuction of the
often disastrous result. In cases of war and passenger vessels,
where a system of exceedingly numerous watertight compart-
ments is adopted, damage to one or more of these compartments
may not produce very serious results, though possibly causing a
list owing to loss of buoyancy, perhaps, on one side only. Being
devoid of this floating support, the centre of buoyancy can no
longer lie in the middle line of the vessel, but in the centre of
the actual remaining immersed buoyancy, though, if the vessel
remain at rest, it follows that the centre of gravity and the centre
of buoyancy are in the same vertical line.
It should be observed, however, that the loss of many vessels,
thoroughly subdivided into watertight compartments, is often
due to the fact that they have so many watertight but unclosed
doors. Collisions generally happen at unexpected moments, and
often in fine weather, when many of these doors are open, with
the result that when the collision occurs, they cannot be reached,
or are entirely forgotten, and hence the result.
Entry of Water into a Compartment beneath a Water-
tight Plat. — Instead of the whole middle compartment being
open to the inroad of the sea after damage to the skin, let us
suppose that a watertight flat or partial deck situated at one-
half the depth of the original draught (5 feet) be fitted as in
fig. 119, and the sea to enter through a hole into the lower com-
partment. Let us now observe the effect upon the metacentric
height. The waterline being entirely intact, the moment of inertia
EFFECT OF ADMISSION OF WATER INTO SHIP*8 INTERIOR. 205
must be reckoned upon the whole area. The metacentre is 3*3
feet above the centre of buoyancy as for the vessel undamaged.
-* ^— — — — — — — — — — ^-— .^— — — — ^.^— — — ..
Fig. 119. — Effect of Entry into a Watertight Compartment
BELOW Partial Deck.
The volume of the lost buoyancy of the compartment B, divided by
the area of the effective waterplane, gives the increase of draught —
2500
2000
= 1 '25 feet = increase of draught.
The centre of buoyancy of the intact end compartments only,
from the bottom, is —
i^jti:?? = 5-62 feet.
2
The effect of the buoyancy above the watertight flat is to raise
the centre of buoyancy for the whole vessel to 6*01 feet above
the bottom.
The metacentre above the centre of buoyancy is 3*33 feet.
The metacentre above the bottom of compartment is 6*01 + 3*33
= 9-34 feet.
The centre of gravity above bottom of compartment is 6*3 feet.
Therefore, the metacentric height is 9*34 - 6*3 = 3 feet, which
is greater than for the vessel in the original intact condition,
and also, as in the foregoing example, where the whole com-
partment between the watertight bulkheads is lost buoyancy.
Moreover, with intact waterline and upper buoyancy, a little
study of the wedges of immersion and emersion will abundantly
prove that in every respect its stability is improved.
Entry ofWater into an Upper Compartment. — But again,
supposing the upper compartment to have been damaged, as in
f^^
Fig. 120.— Effect of Entry of Water into an Upper Compartment.
fig. 120, we shall see that the effect is greatly different. First
of all, the moment of inertia is reduced owing to the loss of the
206 KNOW YOUR OWN SHIP.
space F G. The moment of inertia of the waterplane, and, conse-
quently, the height of the metacentre above the centre of buoy-
ancy, are now the same as in fig. 114, the latter being 2*5 feet.
The loss of buoyancy below the waterline is the same as in the
last case, but the increase of draught is more, owing to the
effective area of the waterplane being reduced by the space F G.
The increase of draught is — ^ = 1'66 feet.
'^ 1500
The centre of buoyancy of the intact end compartments only
above bottom of box is —
lO+i:?? = 5-83 feet.
2
The effect of the buoyancy below the watertight flat is to lower
the centre of buoyancy for the whole vessel to 5*42 feet above the
bottom.
The metacentre above centre of buoyancy is 2*5 feet.
The metacentre above the bottom of the box is 5*42 + 2*5 = 7*92
feet.
The centre of gravity above the bottom of the box is 6*3 feet.
Therefore, the metacentric height is 7*92 - 6*3 = 1*6 feet.
It will be very clear that this case is vastly different from the
previous one, for not only are the metacentric height and free-
board less, but the total loss of the upper buoyancy above the
watertight flat will greatly reduce the effect of the immersed
wedges in producing the levers of stability.
Value of Water Ports. — Effect of water on deck, and necessity
of ample freeing ports.
In well deck vessels of the raised quarter deck type, and also
those with poop, bridge, and forecastle, special care should be
taken that ample means be provided for speedily ridding the
space between the forecastle and the bridge, and also between
the bridge and the poop, of water accumulated through tte
shipping of heavy seas. In addition to the discomfort and the
strain to the structure from such sudden and heavy deck weights,
the vessel's stability may, under certain circumstances, be seriously
affected, and if the water be not rapidly cleared, may prove a
source of real danger. This is easily perceived when we con-
sider the enormous weight which from time to time is poured
on the deck during heavy weather, and this weight being con-
siderably above the centre of gravity of the ship, the effect is
to raise the centre of gravity possibly as high as the meta-
centre.
Suppose a vessel of 2000 tons load displacement has a well
between the bridge and the forecastle 60 feet long, 34 feet
EJ'FflCT? OF ADMISSION Of WAI'EIR iNl'O SHIP S INl^BRIOR. S07
broad, and with bulwarks 4 feet high. This space would hold
60 X 34 X 4
— = 233 tofts. That shipped seas would often entirely
fill this space would be unlikely ; but suppose, for example,
that it be three-fourths filled, the water shipped would w^eigh
175 tons. The centre of gravity of the weight being, say, 10
feet above the centre of gravity of the vessel, the effect is to raise
the position of the latter — -— — — = 0*8 of a foot.
^ 2000 + 175
Supposing the vesseFs metacentric height to be '6 of a foot — not
at all uncommon in many cases of loading — then the centre of
gravity is now approximately 0*2 of a foot above the metacentre,
supposing no rise to have occurred in the height of the latter.
In this condition it follows that the vessel is unable to remain
upright, apart from the influence of the waves, and commences
to heel, the water all rushing towards the inclining side. The
original metacentric height is only regained by the water pouring
over the bulwarks and through the freeing ports, which latter
should therefore be amply sufficient to speedily clear the deck.
The danger will be all the more obvious in vessels possessing
deep wells, the bulwarks of which extend to the height of the
bridge and forecastle, usually about 7 feet. It will be evident
that such a vessel, unless capable of speedily relieving herself of
the water through the water ports, will heel to a greater angle
before getting rid of much of it over the bulwarks. The con-
centration of this water to one side, when inclined, and the
possible synchronism of a wave, may lead to disastrous results.
Certainly, as some reader may suggest, this is an extreme case,
but the fact that so many vessels are, in ignorance, sent to sea
unsea worthy, and so many are recorded annually as "foundered,"
and "unheard of," demands attention, and furthermore proves
that extreme cases are not so uncommon as is often imagined.
Entrance ofWater through a Deck Opening. — Effect upon
Stability owing to the Admission of Water into tJie Interior, either
through a Damaged Deck or Deck Opening. — This case differs
from the previous ones in the fact, that the skin being perfectly
intact, there is no free communication between the water inside
and outside of the vessel. There is, therefore, no loss of buoy-
ancy, the entered water acting directly as deadweight, and
thereby increasing the draught. If this operation were to con-
tinue until the total weight of displacement exceeded the total
buoyancy, the vessel would sink. Should the entered water be
only moderate in quantity, through, perhaps, leakage in the deck
during heavy weather, let us briefly . observe the possible effect
upon the stability.
208
liNOW tOUft OWK Sfll^.
If the vessel be very flat on the bottom, the effect, as Professoi?
Elgar very aptly points out in the paper previously referred to,
will be similar to that of water poured slowly into a box. Water
naturally seeks the lowest position, and this will only be accom-
plished by the vessel inclining, and lowering one of the bottom
comers. At first, only a slight list is perceived, but as the
amount of water in the interior increases, the list continues to
increase until the centre of gravity of the water finds a position
in the vertical line through the centre of buoyancy, after which,
the water, which was previously the inclining element, now
resists further inclination.
Let fig. 121 be a vessel which has gone through these stages of
inclination. If she then remains at rest it proves at once that
the vertical lines through the centre of gravity and the centre
of buoyancy coincide, the centre of gravity having moved from
Fig. 121. — Effect of Water Collected in the Bottom of a Vessel.
G to G', owing to the effect of the shifted water. If a vessel
has more righting moment of stability (righting lever x displace-
ment) at any angle of heel than the inclining moment at corre-
sponding angles (weight of water x perpendicular distance
between g g)* then the vessel will return to the upright. The
vessel in our example (fig. 121) was more tender, for as the
water entered slowly she inclined gradually, thus showing that
the heeling moment of the water was exactly absorbing the
righting moment of the vessel, and thus leaving her, at each
successive angle of inclination, in a state of neutral equilibrium.
She could not heel all at once to her greatest angle of inclination,
simply because the heeling moment was not sufficient to absorb
the righting moment of the vessel until more water had entered.
In fig. 121 let the weight of water in the hold be 50 tons, and
* ^ is centre of gravity of water in upright condition, and ff in inclined
conditioD.
BPPBCT OP ADMISSION OP WATER INTO SHIP's INTERIOR. 209
the displacement of the vessel in this condition 1000 tons. In
the upright condition the centre of gravity of the water was at
g^ but after the inclination it is found to have travelled 6 feet,
to g'. The effect is to draw out the centre of gravity of the
vessel in the direction of the moved water, which distance is
50 x6 n o c I* J.
-j^^=0-3ofafoot.
Owing to the shift of the centre of gravity a distance of 0*3 of a
foot, to, say, starboard side, the effect is the same as deducting
0*3 of a foot from the lever of stability with no water in ; and thus
where the curve of stability shows 0*3 of a foot of lever, there would
in reality be no lever at all, and at this angle the vessel would
lie at rest if undisturbed. If the vessel were forcibly inclined
further, she would probably return to this position again imme-
diately on the inclining force being removed, proving that
beyond this angle her righting moment exceeded the heeling
moment of the water.
If the vessel were now forcibly heeled to the port side and
again left undisturbed, she would lie at the same angle of
inclination as on the starboard side. Should it happen that the
greatest righting lever of the vessel at any angle of inclination
did not exceed 0*3 foot, she would undoubtedly capsize.
The more rise there is on the bottom of the vessel, the less
danger or likelihood is there of water thus taking a permanent
shift, since this form of bottom makes the upright the lowest
position that entered water can find. In such a case, the entry
of a moderate quantity of water is to lower the centre of gravity
and give more metacentric height. But at the same time it will
be remembered that great metacentric height conduces to heavy
rolling, which motion will be transmitted to the water inside,
tending, it is possible, to incline the vessel further than she
otherwise would. These latter remarks apply also to free water
in partially filled water ballast tanks, and show why vessels
which are very tender when light — which tenderness is some-
times further augmented in the operation of coaling — so easily
incline and sometimes take a sudden lurch. This generally
happens at the unexpected moment, so that, as in the case
of the " Orotava," which capsized in Tilbury Dock in December
1896, coaling ports, or side scuttles, or other openings are sud-
denly brought below the water surface, capsizing ultimately
ensuing.
Entry of Water into an End Compartment. — ^Thus far it
will be observed that only the effect upon transverse motion has
been dealt with, and that in the foregoing examples the water is
supposed to have entered into a compartment in the middle of
o
210
KNOW YOUB OWN SHIP.
the length, and thus to have increased the draught uniformly
all fore and aft. However, where a compartment is damaged at
or near the ends of the vessel, not only may there be tendency
to transverse inclination, but longitudinal also.
Thus in fig. 122 let G bo the centre of gravity and B the
centre of buoyancy in the intact condition. Should the vessel
be now damaged through collision in the fore compartment,
C D, and the sea find free entrance, then the buoyancy of this
compartment being lost, the draught must increase, and the
centre of buoyancy will endeavour to shift into the centre of
ftf It
I
^— «» « ^ *^<v •
Fio. 122,— Effect of Entry of Water in Fore Compartment.
the remaining buoyancy, B'. But the centre of gravity and the
centre of buoyancy being no longer in the same vertical line, a
condition of unrest is the result, there being a lever set up
between the vertical lines through these two forces. The vessel
will, therefore, heel longitudinally and go down by the head, and
will not come to rest till the centre of buoyancy is again in the
same vertical line with the centre of gravity. The larger the
compartment damaged, and the greater its distance from the
original centre of buoyancy, the greater will be the change of
draught and trim, with, possibly, disastrous results, for it will
be seen that immediately the stem has gone under water, when
such calamities happen there are possibly several deck openings
or comj)anions uncovered, and the sea finding inroad through
these, adds to the effect by making its way to that end of the
vessel which is inclined.
Height of Bulkheads. — It will now be better understood
why a watertight bulkhead should be placed at a short distance
from each end of all vessels, for these localities are most likely
to suffer in case of collision, and, moreover, being at so great
a distance from the centre of buoyancy, their loss of floating
moment is great. Hence the necessity of carrying all bulk-
heads, and especially watertight ones, as high as possible, in
order to prevent water finding its way over the tops of them
into the next c()ni])artments.
Waterlogged Vessels.— It is not ixxi uufrecjueut sight during
BPPBCT OF ADMISSION OF WATER INTO SHIP's INTERIOR. 211
bad weather in the Baltic, where such a large percentage of the
export trade is in timber, to see an old wooden ship, laden with
timber in both holds and on deck, in a waterlogged condition.
There she lies with a heavy list, rising and falling with each
successive wave, with scarcely ever a movement of her own
(fig. 123).
She has sprung a leak, and water has found its way into her
hold and risen to the level of the sea outside. There being now
free communication between the sea and the water inside, the
whole of the interior space unoccupied by timber — every crevice
Fig. 123.— Waterlogged Timber-ladbn Vessel.
and corner — is lost buoyancy. The result is the draught in-
creases, but not the displacement, until a volume of water has
been displaced by the timber and the framework of the vessel
equivalent to the original volume of displacement. Undoubtedly
the centre of buoyancy has risen. It will now be situated in the
new centre of displacement, which no longer constitutes the
portion of the ship which is immersed and within the skin, but
the centre of the immersed portion of ship and timber unoccu-
pied by water. The centre of gravity has remained stationary.
If the metacentre had remained in the same position relatively
to the centre of buoyancy, the ship, since the centre of buoyancy
has risen, would actually be stiffer than before the leak took
place, when she was probably very tender. The permanent list
proves that such is not the case, and we can rightly come to the
conclusion that a considerable reduction has occurred in the
height of the metacentre.
It has not been caused by the displacement, for that is un-
changed. It can only lie in the moment of inertia of the new
waterline, which is no longer for the whole area of the waterplane
at which the vessel floats, but simply for the sectional area of
actual timber (both cargo and ship) at that waterline. It will
212 KNOW YOUR OWN SHIP,
now be found that the moment of inertia is considerably leaA,
and when divided by the displacement, gives a position for the
metacentre below the centre of gravity. The vessel is, therefore,
unstable, and heels over, and possibly iu some cases, were it not
for the volume of wood on deck, she might capsize altogether.
But she is prevented from this by the effect of the immersed
wedge of timber, which acts as freeboard, giving buoyancy
exactly where it is most needed to keep the vessel afloat.
The effect has been to draw out the centre of buoyancy from
the original position B to B', fig. 123, until the vertical line
through the new centre of buoyancy coincides with the vertical
line through the centre of gravity. The vessel now rests in a
state of neutral equilibrium, having no righting lever of stability
at this angle of inclination.
HAILINQ, SAIL AttHA, BUc!.
CHAPTEtl VI. (SBcriOti Vll.)
SAILING, SAIL ABBA, etc.
Sail Area. — In briefly considering the subject of the capability
of a vessel for carrying sail, our study of " Momenta," Chapter II.,
again proves of great assistance ; moreover, we shall also discover
that sail area is inseparably connected with stability.
fiQ. 124.— TEBKH-UAsTKn SoBOONEa-RiooKS Vbssbl.
Fig. 124 is an outline sketch of a three-masted schooner-rigged
vessel, which will serve as an example for reference.
Sails might aptly be compared to a number of weights ranged
miscellaneously along a lever ; the lever would, therefore, be an
imaginary line passing from the region of the hull to beyond the
topmast sails. Before we could possibly calculate the moment of
pressures about a point at the end of a lever, we should have to
determine the position of the end of the lever from which the
moments are calculated. Exactly the same thing takes place in
dealing with sails ; we must determine the end of the imaginary
lever. This point is called the csiiire qf lateral reeUiance, and
is the centre of the resistance of the water to lateral or broadside
motion. Such movnment would, therefore, be square, or at right
^4 KNOW tbtjR owiJ sttii*.
angles to the forward motion of the vessel, and is usually termed
leeway. The centre of lateral resistance varies in position^ but
it is approximately and sufficiently correct for all practical pur-
poses at the centre of the immersed longitudinal section^ passihg
through the middle line of the ship. In comparing pressures on
sails to weights on a lever, it is not meatit that the actual sail
acts as a weight, but rather the moment of the wind pressure on
each sail, varying according to its distance from the centre of
lateral resistance, has the same effect as a weight on a horizontal
line in giving a bending or heeling moment. The next opera-
tion is to find the centre of this wind pressure for all the sail
area, or, as it is usually termed, the centre of effort. This is done
by multiplying the area of each sail by the height of its centre
from the centre of lateral resistance. Then the sum of all these
moments, divided by the sum of the areas of all the sails, gives
the vertical height of the centre of effort above the centre of
lateral resistance. But it is also necessary to have the fore and
aft position of the centre of effort, and this is obtained by multi-
plying the area of each sail forward of the vertical line through
the centre of lateral resistance by the distance of its centre from
the vertical line. Having found the sum of all these forward
moments, the same operation gives the sum of all the moments
aft of the centre of lateral resistance. The difference between the
forward and after moments, divided by the total sail area, gives
the distance the centre of effort is forward or aft of the centre of
lateral resistance. It will, therefore, be on that side on which
the moments preponderate. (See position of centre of lateral
resistance E, and centre of effort E, in fig. 124.)
We might just notice here that when the centre of effort is
before the centre of lateral resistance, the tendency of the vessel
is to fall off from the wind. This is termed slackness. On the
other hand, when the centre of effort is abaft the centre of lateral
resistance, the tendency of the vessel is to fly up to the wind.
This is termed ardency.
In calculating the position of the centre of effort, only such
sail as could safely be carried in a fresh breeze is calculated
upon, and the sails are all supposed to be braced right fore and
aft. A fresh breeze* is reckoned to blow with a force of 4 lbs.
to a square foot of canvas. Thus the total sail area, multi-
plied by the distance of its centre of effort above the centre of ^
lateral resistance, multiplied by 4 lbs., gives the moment of wind
pressure in foot-lbs. For example, in fig. 124, if the sail area
is 10,000 square feet, and the centre of effort above the centre of .
* The pressure, equal to a fresh breeze, is taken from the British Meteoro*
logical Office Tables.
Sailing, sail ar^a, fiTc* 215
lateral resistance is 50 feet, and the wind pressure on the sails
is 4 lbs. per square foot, the heeling moment of the wind pressure
is 4 lbs. X 10,000 square feet x 50 feet = 2,000,000 foot-lbs., or
2,000,000 Qoo^ ^4.
-? 1 =892 foot-tons.
2240
Now, supposing the displacement of our vessel to be 2000
tons, and the metacentre above the centre of gravity, G M, to
be 2 feet, what will be the angle of inclination with this force
of 892 foot-tons wind pressure? We know that the moment to
hold a vessel inclined at any angle is the righting lever of
stability, GZ, multiplied by the displacement, D, = foot-tons.
We have already got the foot-tons of heeling moment — viz., 892,
so that
?^ = GZ = -^ = 0-44GZ.
D 2000
We also know that GZ = GM x sine of the angle of heel
G Z
for small angles, so that --—-^ = sine of angle,
GM
•44
— - = 0*22, sine of the angle of inclina-
z
tion, and reference to the table of natural sines at the end of
this book shows the angle of inclination to be about 13**.
The effect of setting top sails and top-gallant sails, and all
such light sails, will now be evident.
The higher the sail above the centre of lateral resistance, the
more effect it has in producing large heeling moments, though it
gives no increased propelling power. Thus, when signs of a
squall appear, and all topsails are set, these are taken in first,
for two reasons —
1. If the vessel has a great metacentric height , and is, therefore,
very stiff, when the squall strikes her she offers great resistance
to heeling, with the result that, in such a case, the topmasts are
often carried away, or the sails torn to shreds.
2. If the ship is tender, and has, therefore, a small metacentric
height, the effect of a squall of wind is to incline her to about
twice the angle to which she would have gone if she had steadily
and slowly inclined. Indeed, this would happen in any case.
Many a vessel has been capsized through no other cause than
this. A vessel with heavy yards, etc., is made stiffer by lower-
ing these spare and stowing them on deck. The result is simply
to lower the centre of gravity for the whole ship, and give
greater metacentric height.
A point deserving of notice here is, that as the vessel inclines,
the effect of a horizontal wind pressure will not be so great aa
2l6 ittJoW ifouil OWN sHii*.
in the upright condition, since the surface upon which it blowd
is at an angle less than a right angle. The same applies to sail
which is not braced right fore and aft. However, our reasoning
is sufficiently correct for all practical purposes, and the slight
error, moreover, is on the safe side. Under such conditions,
the angle of inclination is slightly less than it would other-
wise be.
Thus far we have simply considered the effect of a certain
amount of sail in heeling a particular vessel with a given meta-
centric height. But let us view the subject from a different
aspect — viz., in determining some features in the design to carry
a certain amount of sail at a given angle of inclination. From
our previous consideration of the causes affecting metacentric
height, we find that this may be done in two ways. It is known
that great beam produces a high metacentre, and also, that in a
deep vessel with comparatively small beam and low metacentre,
the centre of gravity can be brought down by arranging the
ballast to obtain the position of the centre of gravity required.
The opinion is still in some degree prevalent that a vessel with a
narrow midship section is better adapted for speed than one
with considerable breadth. These erroneous ideas have been
entirely upset by the valuable experiments conducted by the
late Mr. Froude, who clearly showed that of two vessels of
similar length and equal displacements, the one with the greater
beam, and consequently of finer ends, was the better design for
speed. At the same time, this design of vessel, with good beam
and fine underwater form and ends, is the type which can be
made stiffest and most capable of carrying great sail area, for it
not only sends the metacentre high, but in yachts, by placing
the ballast low, the centre of gravity can be brought down.
Frictional Resistance. — From a point of speed, however,
it must be remembered that short vessels encounter greater
resistance from the friction of the water upon the immersed
skin than long ones, the first 50 feet of length being the part which
suffers most from frictional resistance. This is more especially
so when high speeds are attained. After this length the particles
of water, having partaken of the onward motion of the vessel,
naturally offer a diminished resistance. Up to about 8 knots,
from 80 per cent, to 90 per cent, of the total resistance is due to
skin friction.
The necessity, therefore, of keeping the bottoms of vessels
clean is most important, as a rough surface adds immensely to
the amount of resistance, a surface of the smoothness of calico
offering approximately twice the resistance of a varnished siuface ;
and, of course, sand about two-and-a-half times the resistance of
SAttlKG, dAlL AB^A, Eil^C.
217
Vatnish. fieyond these speeds, other resistances become very
important, frictional resistance diminishing to 50 per cent, or 60
per cent, of the total.
Wavemaking Resistance. — This is found most in vessels of
bluff form at the ends, simply because, especially at the fore end,
the head resistance offered by the bluffness, corresponding to a flat
board moved as shown in fig. 125, causes the water to rise up in
front of the vessel, and the making of this wave means expenditure
and loss of power. It is not uncommon in vessels of the bluff
cargo type, of not more than 9 knots
per hour, to create a considerable wave
6 or 8 feet in front of them.
In vessels bluff at the after end,
waves are also created at the stem,
though not to such a marked extent ;
but something else occurs which gives
rise to another resistance — viz. : —
Eddy-making Resistance. — ^This
is similar to the effect of the flat board
moved as shown in fig. 125. After the
water has poured round the edges of
the board it eddies behind it, and
travels in the direction in which the
board is moved. All the energy needed
to produce this is loss of power. Just
so is it with our actual ship. The
eddying water being dead, the rudder
is rendered less efficient, and if the
vessel be a screw steamer the propeller is also less effective ; so
^hat, while it is most essential for speed to have the entrance of
the fore end fine, it is of paramount importance to have the run
03;- the aft end fine, as there is the danger of a double resistance —
wave and eddy-making — which for high speeds assumes enormous
proportions.
Coming back to the subject of design, let us take a yacht 100
feet long, with a displacement of 200 tons, and a required sail area
of 5000 square feet. This would represent, at the rate of 4 lbs.
per square foot, a sail pressure from wind of
Fig. 126. — Wave and
Eddying made by Moving
A Flat Board through
Water,
4 lbs. X 5000
2240
8*9 tons.
Let the estimated height of the centre of effort above the centre
of lateral resistance be 40 feet, then 40 x 8*9 = 356 foot-tons
heeling moment. This must be balanced by the stability at,
say, a required angle of inclination of 15°.
Sl^ KNOW tOtJR oWn" mt^.
First, we must find the righting lever of stability at' tliis
angle —
Displacement x lever, or G Z = moment,
then, Moment ^ j ^^^^
Displacement
therefore, ?5^ = 178 = GZ.
200
The next operation is to find the height of the metacentre,
G M, above the centre of gravity, which will give 1*78 = G Z.
The rule is, G M x sine of the angle of heel = G Z,
then - . %^ . =GM,
sine of angle
the sine of IS** = 0-258 ;
1*78
therefore, — -—= 6*9 feet metacentric height.
0-268 *
In yachts there is the alternative, where the displacements are
equal, as to whether it is better to get metacentric height by-
beam, with more or less draught and less ballast, or by increased
depth and draught, and less beam and more ballast. On this
point, as the designs of recent fast racing yachts prove, naval
architect experts differ in opinion in some degree.
However, in sailing-ships, where it is not possible to regulate
and fix the centre of gravity as on a yacht, whose conditions are
fairly constant, but which, on succeeding voyages, carry cargoes
of varying densities, it becomes necessary to give sufficient meta-
centric height and stiffness by means of beam.
In some cases double bottoms are fitted for water ballast, but
this is not the common practice, since, when the holds are full and
the tanks empty, the effect of the double bottom is to raise the
centre of gravity of the cargo, and tend to make the vessel tender.
The combined effect of lofty masts and great sail area unite to
necessitate greater stiffness.
SiPAfetLiTt It^FORlktADtoK.
SIS
C it AFTER Vl. (Skction VIIL)
STABILITY INFORMATION.
What stability information should he supplied to a commanding
officer?
It would be rather a difficult matter to answer this question
to the satisfaction of every naval expert, and non-expert, since
the purposes for which vessels are built vary so much in their
30' •♦o* so'
Scale of Degrees.
A, Curve for fully equipped condition.
B, Curve for coal and stores consumed.
70'
SO'
—I
90'
Angle of Maximum Stability. A, condition.
Fig. 126.— Curves of Stability of a Steam Yacht.
nature. But it appears that the commanding officer, after
making himself thoroughly acquainted with the principles of
the subject, and fully aware of the possible exigencies which his
vessel may meet, is the fittest and most capable person to decide
what information is required. It is scarcely necessary at this
stage to state that officers of all vessels do not need the same
information. In the case of a yacht whose condition is practically
220 KNOW tOUR OWN SfilP.
constant, the only change arising from the consumption of bunkeif
coal and stores, scarcely any iiiformation is required, as such a
vessel can be designed and built to fulfil certain conditions and to
possess a definite amount of stability. At most, therefore, two
curves, showing her righting levers and range, in the light and
equipped condition, can be of any value in satisfying her captain
of her reserve safety. Fig. 126 represents the curves of a steam
yacht 152 feet long, 22 feet beam, and 13 J feet deep.
Then, again, other vessels are built for special trades, and the
exact natures and densities of their cargoes being thoroughly
understood, the naval architect is able to produce a design such
as will ensure certain conditions of seaworthiness in the loaded
condition.
But by far the majority of vessels are built to carry miscel-
laneous cargoes, those known as tramps carrying anything and
everything, anyw^here. So that while it is impossible to design
and build a ship specially adapted for every trade, it lies in the
power of the naval architect or shipbuilder to provide such
information as will greatly help the conmianding officer in under-
standing what condition of loading and ballasting to avoid, and
what to adopt, to best make his particular vessel seaworthy.
The method of supplying curves of stability, adopted by Messrs
J. L. Thompson & Sons, Ltd., of Sunderland, is certainly a most
commendable one. Figs. 106 and 107 show sets of curves provided
by them for two of their steamers.
In addition to the information on these curves in the case of
general carrying vessels, there might be provided with great
advantage and profit to the ships' officers the following, viz. : —
(V) A curve of stability wJien floating at the load draught with
the least metacentric height compatible with safety, as a guard
against making the vessel too tender.
(2) -4 curve showing the stability ivhen loaded to tlie hatches with
the lightest homogeneous cargo likely to be carried of specified
density or cubic capacity per ton, with a statement of the amount
of ballast to be carried in order to ensure safety and produce the
best behaviour. (But it does not follow that the vessel should be
ballasted down to her load waterline to obtain such a condition.)
(3) ^ curve of stability with the heaviest cargo likely to be
carried of specified density or cubic capacity per ton weight,
together with a statement of how such cargo should be stowed
in the holds and 'tween decks, so as to ensure sufficient stability,
and the best behaviour at sea.
(4) An intermediate cutuefor a cargo of medium density y and a
statement of the quantity of ballast, if such is required, to pro-
duce the best results.
STABILITY INFORMATION. 221
(5) A most important curve is that showing the best condition
of a vessel light and in ballast, with an exact statement of the
amount and position of ballast to be carried to ensure such a
condition. .
In these days, when water ballast is so extensively used, a
great amount of ignorance is evinced as to how and where it
should be stowed to secure the desired results. In some cases
water ballast is carried only in fore and after peaks, with as little
temporary ballast as possible in the holds. The effect of this
in straining the vessel has already been pointed out. The
commonest method is to fit water ballast tanks throughout the
whole or part of the length of the bottom, and to fill them all
up when light, regardless of the diffierence in type, proportions,
etc., and the result is that officers often have to complain of
their vessels almost rolling their masts overboard. A glance at
figs. 106 and 107 very clearly indicates what would be the
probable behaviour of these vessels at sea, light or with their
ballast tanks full. Curves A and B show the stability levers of
the vessels light, and C and D with the ballast tanks full. In
all these cases, and especially in fig. 107, the levers are very
long for small angles of inclination ; in fact, the vessels have too
much stability, with the natural and consequent result that
heavy rolling would most probably be experienced. We are
thus driven to the truth that the bottom of the ship is not
always the proper place for all the ballast. As previously
explained, a better principle sometimes adopted is to fit very
deep tanks in the region of amidships, which, while increasing
the displacement, also mitigates the evil of excessive stability.
222 KNOW TOUR owjir shi?,
CHAPTEK VL (Section IX.)
CLOSING REMARKS ON STABILITY.
General Results. — Before concluding our considerations of the
various aspects of the subject of stability, it may be advisable
to gather up, as briefly as possible, a few of the most important
facts which have been revealed.
The centre of buoyancy is the centre of gravity of the displaced
water, at whatever angle the vessel may be inclined, and tlm)ugh
which the upward vertical pressures of buoyancy act.
The transverse metacentre is the point where the vertical line
through the centre of buoyancy for indefinitely small angles of
inclination intersects the middle line of the vessel (such middle
line being the line through keel and masts), and is also the point
above which the centre of gravity must not rise, in order that
a condition of stable equilibrium may be maintained. It is
influenced chiefly by beam.
The metacentre and the centre of hvxyyancy vary in position
with every variation of draught, but always occupy the same
respective positions at any particular draught. Their exact
positions, when floating upright at any draught, are found from
curves obtainable from the shipbuilder or naval architect.
The centre of gravity is the centre of the total weight (not
bulk) comprising a ship and her entire equipment and cargo.
It may, therefore, occupy widely different positions for the same
draught, according to the high or low positions of the weights
carried. The centre of gravity is found by experiment, as pre-
viously explained in this chapter.
The distance between the centre of gravity and the metacentre
is termed the metacentric height.
Metacentric height in feet, multiplied by the sine of any angle
not exceeding 10° or 15° for ship-shaped vessels, gives approxi-
mately the righting lever of stability, in feet, for that angle.
Righting lever in feet, multiplied by displacement in tons, equals
rig] 1 ting moment in foot-tons.
Metacentric height, or metacentric stability, is held to be
unreliable beyond the small angles previously stated, as it may
continue to grow both in the length of the levers and in the
CLOSING EBMABKS ON STA6ILITT. 22B
extent of the range, or it may rapidly decrease and vanish
altogether^
The lefoer of stability can be ascertained at any angle of inclina-
tion by finding the position of the centre of buoyancy at that
angle. The horizontal distance between the vertical lines
through the centre of buoyancy and the centre of gravity indi-
cates the righting lever. If the vertical line through the centre
of buoyancy intersects the centre line of the vessel (that is, the
line passing through the keel and masts) above the centre of
gravity, the lever is a nghting one ; if it intersects below the
centre of gravity, the lever is an upsetting one.
A diagram, showing the levers of stability at all angles of
inclination when in any particular condition, indicating both
the angles of maximum levers and vanishing point of stability,
is termed a curve of statical atahility^ and is also obtainable from
the naval architect or the shipbuilder.
Large metacentric height indicates great stiffness^ and small
metacentric height tenderness.
Stiffness can be obtained in designing a ship by increasing
the beam, and thereby raising the metacentre ; and in an actual
vessel already built, by lowering the weights on board and
bringing down the centre of gravity.
If the range of a vessePs stability is known at the load
draught with a certain metacentric height, any reduction in
that height, which can only be effected through the centre of
gravity, means reduced range and reduced levers of stability,
and any increase produces both increased level's and range.
Similar metacentric heights at different draughts produce
widely different conditions of stability.
Freeboard is also a powerful agent in influencing a vessel's
stability, but by itself is no guarantee for either the range or
the length of righting levers. The greater the freeboard, com-
bined with a fixed position for the centre of gravity and a fixed
draught, the longer become the righting levers at considerable
angles of inclination, and also the greater the range.
At light draughts, even good metacentric height (such as
might be admirably adapted for load draught) and great free-
board may only produce small range and levers of stability.
Great stiffness creates rapid movements among waves, and
tends to heavy rolling, while tenderness conduces to slow, easy
movements, and general steadiness.
All vessels endeavour to float among waves in a position
perpendicular to the wave surface. How far they succeed, de-
pends chiefly upon the ratio of their period of oscillation in still
water to the period of the waves among which they are moving.
224 KNOW YOUR OWN SHIP.
By a vessel's period of oscillation -is meant the time taken to
perform one complete roll, that is, say from port to- starboard^
when forcibly inclined in still water. The period for large and
small angles of roll is approximately the same.
By the wave period is meant the time occupied in the passage
of two successive wave crests past a stationary object.
When the period of oscillation is less than half the wave
period, the vessel will roll with the waves, approximately main-
taining herself perpendicular to their surface, being upright at
their summit and trough, and at her greatest inclination on the
steepest part of the wave slope. This could only be accom-
plished by vessels of extraordinary beam to depth, and also
when the beam is comparatively small in relation to the length
of the waves, but is exactly the manner in which a small raft
would float among waves.
Although it is most uncommon to find vessels so rapid in
their movements as to have their period of oscillation less than
the half wave period, it is not so uncommon to find vessels
which have been made so stiff" as to have a roll period of probably
half the period of the waves they are likely to fall in with, pro-
ducing s^ynchronism with the waves, or, in other words, keeping
time, and thus when at their greatest angles of inclination, they
receive the impulse of the wave, they answer by taking a
tremendous lurch.
Synchronism may also occur periodically on a series of waves.
When it is remembered that waves in different localities, and
at different times, vary both in length and period, it will be seen
that it is scarcely possible to always escape the effect of
synchronism, however a vessel may be loaded. It should be
noted that in vessels made excessively stiff", the probability of
synchronism is greatly increased, and on the other hand, with
the slow rolling ship, though it is not imlikely that occasionally
she may fall in with waves producing the same effect, neverthe-
less, taking her all round, she is certainly the steadier and more
comfortable ship.
Slow rolling motion^ which is conducive to steadiness, may be
obtained chiefly in three ways : —
1. By small metacentric height.
2. By means of resistance agents on the immersed skin in the
form of bilge keels.
3. By winging out the weights from the centre to the sides of
the vessel.
The two latter of these are very safe methods, since they make
no deduction from the vesseVs stability. The first, however,
necessitates a correct understanding of the vessels dealt with.
CLOSING BBMABKS ON STABILITT. 225
for, as previously stated, any reduction of metacentric height
produces both shorter levers and range. Moreover, what is
safe and good for one ship may be exceedingly dangerous for
another, hence the necessity of correct information being pro-
vided by the designer, and received by the commanding oflBcer,
in order to ensure safety.
Synchronism among waves upon a vessel of very small meta-
centric height and slow rolling period may cause her to reach
large angles of inclination, and if the levers and range are very
short, will greatly increase the possibility of her capsizing.
Bad loading may thus produce both the dangerous extremes —
excessive stiffness with heavy rolling, and too much tenderness
with great lack of necessary stability.
Synchronism may be destroyed by altering the speed or
course.
226 KNOW YOUR OWN SHIP.
CHAPTER VII.
TRIM.
Contents. — Definition— Moment to Alter Trim — Change of Trim — Centre of
Buoyancy of Successive Layers of Buoyancy at Successiye Draughts —
Longitudinal Metacentre — Longitudinal Metacentric Height — Moment
to Alter Trim One Inch — Practical Examples showing how the Change of
Trim is Ascertained.
Under certain circumstances — cases of emergency, accidents to
propeller and shafting, entering docks, etc., it often becomes
necessary to decrease the draught of a vessel with or without an
alteration to trim, or to simply alter the trim by putting the ship
down by the head or the stern as may be required. (Trim is the
difference between the draughts as indicated at the stem and
stem.)
Trim is a subject of e very-day consideration to the scientific
designer, and is so inseparably related to stability that, in order to
obtain the best results, they must be dealt with simultaneously.
However, in dealing with the subject it is assumed that due
regard has been paid to stability in the vertical distribution
of the weights of the cargo, and our attention is directed to the
longitudinal distribution of weights, whether they be in the form
of cargo in the holds, or water in the trimming tanks.
Sometimes, in a specification for a new vessel, a shipowner
inserts a clause to the effect that his vessel when loaded with a
homogeneous cargo, must trim in a certain condition, say, 1 foot
by the stem.
At first sight this might appear an awkward condition for a ship-
builder to guarantee. But with a thorough grasp of the principles
of buoyancy and gravity it is very simple, though it may entail
considerable labour and time in order to get an accurate result.
Where a high speed is required, the under-water form of the
vessel is designed to the stipulated draught regardless of internal
arrangement of holds, position of engines and boilers, etc. When**
this is completed, having secured the displacement required and
the best form of lines for high speed, the longitudinal position of
the centre of buoyancy is calculated, and the designer knows that
the weights constituting the hull and equipment of the ship,
TRIM. 227
including engines and boilers, and the holds loaded with homo-
geneous cargo, must be so arranged that the centre of gravity of
the whole must be vertically over the centre of buoyancy. When
such a condition is fulfilled, no doubt rests as to the trim of the
ship when she is built and loaded.
Everyone knows that to shift a weight forward or aft along a
ship's deck will produce some alteration to the trim. If the weight
is moved forward, as in fig. 127, where 10 tons are shifted 60 feet,
Fig. 127.— Change in Teim oaitsbd by moving a Weight
FORWARD ALONG A Sh1P*S DeOK.
the vessel must have increased in draught at the stem, or, as we
say, "gone down by the head," and, consequently, as the mean
draught remains practically the same, she must have risen by the
stem. As the effect upon the trim for a particular ship at a
certain draught depends almost entirely upon the amount of the
weight and the distance it is moved, the moment obtained by
multiplying the one by the other (10 x 60 = 600) is termed the
" moment to alter trim" However, this quantity gives little idea
as to what the exact change in trim will be, especially when it is
remembered that the same moment will produce different results
at different draughts, and by itself it is therefore practically use-
less. Could we discover a moment that would give 1 inch change
in trim at the required draught, then the problem is solved, for it
would be simply a matter of finding how often the moment to
change trim 1 inch could be got out of the total moment to alter
trim, and the result would be change of trim in inches.
It should be clearly understood that " change of trim " means
the change in draught at stem added to change at stem and vice
versa. A ship floating at, say, 10 feet draught forward and 11
feet aft, changes trim owing to the shifting of weights on board
and the new draught is 10 feet 1 inch forward and 10 feet 11
inches aft. She has gone down 1 inch by the head and risen 1
inch by the stem. The change in trim is 2 inches.
How to obtain the moment to change trim 1 inch we shall
investigate shortly.
Let fig. 128 be a ship floating at the waterline a b. The centre
228 KNOW TOUR OWN SHIP.
of buoyancy is at R One condition for a vessel to float in a state
of equilibrium is that the centre of buoyancy and the centre of
gravity be in the same vertical line, considered both transversely
and longitudinally. If this be a ship's condition as regards the
transverse centre of buoyancy, and with the metacentre above the
centre of gravity, she floats upright in a condition of stable
equilibrium, and the vessel will incline to neither one side nor the
other, except by the application of exterior force. Sometimes,
.^
t
.B
1
Fig. 128. — Illustrating the Alteration in the Fore and Ajt Posi-
tion OF THE Centre of Buoyancy of the Suoobssive Laybbs ov
Buoyancy caused by Increased Immersion.
however, probably owing to the shifting of weights on board, the
ship will only And a condition of rest after she has inclined to an
angle of greater or less degree ; in short, till the centre of gravily
and the centre of buoyancy are again in the same vertical line.
When a vessel is launched, she at once seeks a position of rest
such as we have described. Transversely, she most likely floats
upright, but, looking at her fore and aft, we often find that she
heels, perhaps several degrees either towards the stem or the stem,
or, as we say, " trims " either by the stem or the stem.
Let fig. 128 represent the condition of a ship just launched,
trimming, say, 2 feet by the stem at waterline a b, and B is the
fore and aft centre of buoyancy. It is clear, then, since the vessel
floats in a condition of equilibrium, that the centre of gravity is in
the same vertical straight line as the centre of buoyancy, and thus
we at once have the longitudinal position of the centre of
gravity.
Suppose we wish to load such a vessel without altering the
trim. Naturally the draught increases as the loading proceeds.
The question is : — Where should the additional weight of the
cargo be placed 1 and it is exactly at this point where many
blunder. The assumption often worked upon is, that the centra
of gravity of the added weight should be placed in the same
vertical line as the centre of gravity and the centre of buoyancy
when floating at the original draught. Were a ship as regular
in shape as a box, such an assumption would be quite right;
but for ships it is utterly wrong, for were such a method carried
out, it is not at all unlikely, in many cases, that the trim would
\
TRIM. 229
have altered — the reason is not difficult to ascertain. Let us
suppose that the cargo has to be loaded in four instalments of
equal weight, putting the vessel down successively to the water-
lines cd, e/, g h, j k. Though B is the fore and aft position of the
centre of buoyancy at the waterline a b, it does not follow that it
will occupy the same fore and aft position at the waterline c d.
If the ship trims considerably by the stern, it may be found that
the centre of buoyancy of the layer of displacement between the
waterlines a b and c d may be some distance aft of B, so that to
immerse this buoyancy, the centre of the added weight must be
placed over the centre of its own particular buoyancy B' or equally
distributed on each side of B'. Similarly, the centre of buoyancy
of the next layer of displacement may not be over either B or B^,
but at B^, and thus the next instalment of cargo must be placed
over B2 in order to put the ship down bodily and not alter the
trim, and so on up to the load waterline.
In order to make further comprehensive these counterbalancing
forces of weight and buoyancy, let us take another illustration.
Suppose our ship to be floating at rest in a light condition at the
waterline a b, fig. 128. The centre of buoyancy is at B, and the
centre of gravity is at a point vertically above it. Here we have
the whole weight of the empty ship supported by all the buoyancy
below a b. One hundred tons of cargo in quantities of 10, 15, 30,
20, and 25 tons are to be placed on board in such positions as to
cause no alteration to trim, the vessel having to float at the water-
line c d, which is parallel to a b. It is evident, therefore, that
the volume between a b and c d must measure 100 tons of floating
power or buoyancy. So that what we have to deal with is
not the original buoyancy below a b, nor the light weight of the
ship. These drop out of our consideration altogether. Our
attention is directed to the 100 tons of weight, and the 100 tons
of buoyancy which has to support it. Let B^ be the centre of this
100 tons of buoyancy; the centre of the 100 tons of cargo must
be placed in the vertical line which passes through B^, it matters
not whether the weights be on deck or in the bottom of the hold,
the centre only must be, as stated, in the same vertical line with
BK
Let us proceed to load.
The 10 tons
are
placed 5 feet abaft of B^
))
15
>»
80
1)
it
80
i»
24
II
>}
20
II
40 „
forward „
The question arises, " Where should the 25 tons be placed in
order to get the vessel to the trim required *{ "
230 KNOW YOUR OWN SHIP.
Moments aft. Moments forward.
10 X 5 = 50 20 X 40 = 800 foot-tons.
15 X 30 = 450
80 X 24 = 720
1220 foot-tons.
1220 - 800 = 420.
We still require a moment forward of 420 foot-tons in order to
equalise the moments of each side of B\ and this has to be
obtained by placing the remaining weight of the cargo, 25 tons, in
such a position as to produce this.
Weight X distance from B^ = moment in foot-tons, therefore,
— ;-T- - = distance from B^ that the 25 tons must be placed,
weight
^ = 16-8 feet, distance required.
To the average ship's officer considerable difficulty presents
itself in carrying out a method such as that just described. He
asks, how is he to find the centre of buoyancy of the layer of
buoyancy which is immersed, owing to the addition of a certain
weight. It is true that there are ships* officers who, far ahead of
their profession in the knowledge of ship theory, have had them-
selves provided with the lines plans of their ships, from which
they can ascertain the form of the whole or any section of their
vessels. Without such a plan the centre of buoyancy of any
particular layer of buoyancy could not be found. However, it
is not intended to propose any such process as an every-day,
practical, handy method for seamen. But, imderstanding the
fiuidamental principle, a simple, practicable, and reliable method
may be deduced. Where the increase in draught is not very
great, instead of finding the centre of buoyancy of such a layer as
that between a b and cd in fig. 128, it is sufficiently correct for all
practical purposes to find the centre of gravity of the waterplane
a &, and take this as the approximate position of the centre of
buoyancy. From this point calculate the moments of the weights
of cargo placed on board. Here, again, for any seaman to have to
calculate the centre of a waterplane,* whenever he desired to
estimate the trim, would be out of the question. But the second
difficulty can readily be overcome, for just as easily as a curve of
displacement, or a curve of " tons per inch " is made, can a curve
of centres of gravity of waterplanes be constructed, and, by this
means, the centre of any waterplane between the light and load
draughts can be ascertained. This could, with little trouble and
at the expense of little time, be supplied by the shipbuilder or the
* Rules for exact calculations and worked examples are found in Chapter X,
on " Ship Calculations,"
231
Curve 1, fig. 129, is euch a curve for a steamer 352
J a feet by 28 feet. ITie vertical scale represents draughts,
the horizontal scale, distances of centre of gravity of waterplanes
from after aide of after stern-post.
It must be understood that all centres of gravity so found will
be for waterplanes parallel to the keel only, and are only strictly
correct when taken for a vessel floating upon even keel. When a
ship trims slightly by the stem or the stem, the result* obtained
by using the distances from this curve would be practically correct.
BoIeotD
etu
cet
from alUr .Ide of 8lam-Po.t.
_« « x__
H»« MiWMjBjaljWOTWa
,«-»» 1
1
31
1/
\
?
m
u
i
W
U
n
J
1
w
1
T
IT
r
Fio. J2B.— CuEVBa OF Cbiitebs ot GaAvirr of Watirplaweb.
No. 1. Oh Even Keel.
No. 2. TeIMMINO a FEET B^ THE STEBH.
Where, however, a vessel trims very much by the stem, these
distances may be considerably in error. In order to come nearer
the truth, it might be advisable to have another curve, No. 2, on
our dii^;ram, calculated for the same mean draughts, but with the
ship trimming 6 feet by the stem. This curve would show the
centres of gravity further aft. With these two curves, and the
exercise of a little judgment, it is possible to fix the position of the
centre of gravity of any waterplaiie in any condition of trim with an
exactitude amply sufficient for all practical and working purposes.
Let it be understood that when only a weight already on board
is shifted, the moment altering the trim is simply the product of
232 KNOW YOUR OWN SHIP.
the weight and the distance it is shifted. But when a weight or
weights are placed on board in certain positions, or are taken out
of a ship, then these weights are multiplied by the distance between
their centres and the centre of the waterplane. If the weights are
placed forward of this point, then the moment obtained tips the
ship forward ; if the weights are aft, the moment tips the ship aft.
If some of the weights are placed aft and some forward, then the
difference between the fore and aft moments gives the moment
altering the trim. When weights are discharged from a ship for-
ward, the result is a moment putting her down by the stem, and
vice versd when weights are discharged aft. Naturally, discharging
weights decreases the mean draught, while alteration to trim may
also be caused.
The centres of gravity of the waterplanes, from which are
taken the distances in order to get the moment to alter trim,
have been very aptly called the " tipping centres," and in future
we shall adopt this handy and expressive term.
Having, it is hoped, made clear how to ascertain the moment
to alter trim, our next step will be to find what the exact altera-
tion to the trim is.
When a ship is moderately inclined transversely, the stifihess is
measured by the metacentric height, and thus, the greater the
metacentric height, the less inclination will be caused by the
transverse shifting of a weight on board. A vessel, considered
either transversely or longitudinally, will have the centre of gravity
at the same height from the keel, in any particular condition of
loading or ballasting. The centre of buoyancy also is at the same
height in both cases.
But, in turning to the metacentres, there is a great diflFerence
in their positions. Transversely, the metacentre Varies from a
few inches to a few feet above the centre of gravity for passenger
and cargo steamers. But longitudinally, for the same vessel, it
may be as high, or higher, than the vessel is long.
Metacentre above centre of buoyancy
_ Moment of Inertia of Waterplane.
~ Displacement in cubic feet.
We have only one displacement, as we have only one ship
with which to deal, so that the diflference must lie in the moment
of inertia of the waterplane. And yet we have only one water-
plane, and one area for both transverse and longitudinal considera-
tions. Then it is evident that the moment of inertia for longi-
tudinal inclination cannot be similar to the moment of inertia for
transverse inclination, and this is so.
TRIM.
233
For transverse inclination, the moment of inertia is calculated
about the fore and aft middle line of the particular water-
plane. For a rectangular waterplane the moment of inertia is
Length x Breadth^
12 •
But for longitudinal inclination, the moment of inertia is
calculated about the transverse axis passing through the centre of
gravity of the same waterplane, and for a rectangular figure the
. « . _^. ij , Length^ x Breadth
moment of mertia would be ^ — .
Taking the length of a rectangular waterplane as 100 feet and
the breadth 20 feet the moment of inertia for transverse inclination
would be 6 6 6 6 6 (draught 10 feet), and metacentre above centre
Fig. 130.
of buoyancy, 3 '3 feet ; and for longitudinal inclination, 16 6 6 6 6 6,
and metacentre above centre of buoyancy, 83*3 feet. This enormous
longitudinal stifihess possessed by ordinary cargo and passenger
vessels explains why they are so much more easily inclined trans-
versely than longitudinally, either by the application of exterior
force, or the shifting of weights on board. Let fig. 130 represent
234 KNOW YOUR OWN SHIP.
a vessel floating at the waterline "W L, in which condition G is
the centre of gravity, B the centre of buoyancy, and M the meta-
centre. A weight at P is shifted horizontally a distance of d to
T. The vessel alters trim so that W^ L^ is the new waterline, B^
the new centre of buoyancy, and G^ the new centre of gravity
which has travelled in a direction parallel to a line joining the
centre of the weight in the original and new position. The
vertical line through B^ and G^ intersects the originally vertical
line through B and G at M, the metacentre. Let the waterplanes
intersect at the point O, which for moderate inclinations is the
tipping centre. Here we have now three triangles G M G^,
W W^, L L^, whose angles are similar.
G Gi = ^. , P X ^ .
Displacement in tons
G G^ also = G M X tan angle M,
then tan of angle M = or
G M D X GM
D = displacement in tons.
Similarly in triangle L O L^ we have : —
L L^ = O L X tan of angle 0, but angle O = angle M,
therefore L L^ = L x _ , ■ or
G M D X GM'
and similarly in triangle W W^ we have
W Wi = W X tan of angle 0,
or W Wi = W X -^-^^JL,
D X GM
And for a total change of trim we have
W Wi + L Li - W L tan of angle
Assuming that a certain weight P moved a certain distance
gives 1 foot change of trim, then -— ofFxd will equal the moment
1^
to alter the trim 1 inch, and this is the moment it is usual to find.
The formula will now be :
1/wT V X d \ ^ , DxGM
— I W L X I or P X a = = moment to
12 V DxGM/ W L X 12 "'"""*'"*' "^
alter trim 1 inch.
The only factor in this formula for moment to alter trim 1
inch which presents any difficulty to a ship*s officer is G M — the
longitudinal metacentric height.* But this can be overcome by
* See Chapter X. for rules for the calculation of the height of the longi-
tudinal metacentre.
TBIM. 255
obtaining from the builders or deBigners a curve of longitudinal
metacentres. This is interpreted in exactly the same manner as
the curve for transverse metacentres. Fig, 131 is such a curve.
Knowing the position of the centre of gravity in a light, and
perhaps one or two other conditions, it will be an easy matter to
roughly approximate the position of the centre of gravity in any
other condition. With so great a distance between the longi-
J \
J \ __
.L_____\--
i \
M n V m: T. SI js m jbjt h am a t
Sole o( DnughtB.
FiQ. 131. — Cttbve of Lonoitudinal METAOENTBaa.
tudinal mefacentre and the centre of gravity, an error of a foot or
so in approximating the position of the centre of gravity would
make practically little difference in the final result. A few
examples are now given illustrating the application of these
methods.
To calculate the effect upon the trim of filling or emptying
236 KNOW YOUR OWN SHIP.
trimming tanks, the centre of gravity of each separate tank ought
to be known ; this could easily be supplied by builders, together
with the exact capacity of each. The same remark applies to the
filling and emptying of bunkers.
Example I.
A ship is 352 feet long. The displacement is 6200 tons on a
draught of 20 feet aft and 18 feet forward. The mean draught
is therefore 19 feet. At this draught, it is found by referring to the
metacentric diagram (tig. 131) that the metacentre is 460 feet above
the keel. By approximation, the centre of gravity is 16 feet
above the keel. 460 - 16 = 444 feet metacentric height. The
length of the waterline is about 352 feet. Then ^^^ — — = 651
^ 352 X 12
moment to alter trim 1 inch.
One hundred tons of cargo are taken out of an after-hold and
placed in a fore-hold, the distance moved being 100 feet.
Required — alteration to trim.
100 X 100 = 10,000 = Moment to alter trim. Then
- '--— = 15J ins. = Total change of trim.
651 *
Should the tipping centre be at or near the middle of the length,
then the amount of immersion at the fore end and the amount of
emersion at the after end will be equal, the draught forward
being 18' 0" + 7| = 18' 7|", and aft 20' 0" - 7f" = 19' 4f".
However, as previously shown, this could be ascertained with
considerable accuracy by referring to the curves of centres of
gravity of waterplanes.
It is found, ^g. 129, that the tipping centre is 175 feet from the
after side of the stem-post, and it will be 177 feet from the fore
side of the stem. Under such circumstances the inunersion at the
fore end and the emersion at the after end will be practically equal.
Where the difference is considerable the immersion and emersion
at the ends is proportional to the two lengths making up the whole
length of the w^aterline.
Supposing an error of 2 feet had been made in estimating the
position of the centre of gravity, and instead of the metq,centric
height being 444 it should have been 442, the effect upon the total
alteration of trim would have been less than ^ inch, which in
practice would not be a serious error.
Example II.
We will take the same vessel \mder similar conditions, floating
at the same original draught, 20 feet aft, 18 feet forward.
TRIM. 237
Suppose we were asked how far to shift the 100 tons forward
to bring the ship upon even keel. That is, the trim has to be
altered 24 inches.
We found that the moment to alter trim 1 inch was 651,
therefore the moment for 24 inches will be 24 x 651 = 15624,
15624
= 156 feet, distance 100 tons has to be moved forward.
Example III.
Again, taking the same vessel floating at the same waterline
under the same conditions, let the main double bottom tank
now be filled. The tank contains 210 tons of water. Required —
the effect upon the trim. It is clear that the draught must
have increased. In making the estimation for alteration to
trim caused by placing a weight on board a ship, it is always
assumed that the weight is first placed over the centre of gravity
of the waterplane at which the vessel is floating. This, as we have
seen, increases the draught uniformly, when the weight is small
compared with the displacement of the ship. The weight is then
shifted to its proper position, and the alteration to trim found, as
shown in the foregoing examples. Referring to the scale or curve
of "tons per inch," which, along with capacities and deadweight
scales, is often, or should be, supplied to ships, the tons to increase
draught 1 inch is found. Let the " tons per inch " be 30, then
210
""— = 7 inches increase in draught by filling the tank.
The new draught is 18 feet 7 inches forward, and 20 feet 7 inches
aft. At this draught, we find, from the curve of longitudinal
metacentres, the height of the metacentre, and again we approxi-
mate the position of the centre of gravity, taking account of the
210 tons in the bottom tank.
The metacentric height is now 434.
Then = 658 moment to alter trim 1 inch.
352 X 12
The distance from the centre of gravity of the tank to the
tipping centre is 60 feet. Then, 210 x 60 = 12600 =» moment to
alter trim.
— -— =19 inches total alteration to trim.
Supposing the ratio of the length of the waterline before the
tipping centre to the length abaft be as 8 to 7, then the alteration
to draught at each end of the vessel will be 10 inches forward, and
9 inches aft, and the ultimate draught will be 18' 7" + 10" = 19' 5''
forward, and 20'-7" - 9" =- 19'-10^ aft. The effect upon trim of
238 KNOW YOUR OWN SHIP.
loading a moderate quantity of cargo or filling bunkers would be
calculated in a similar manner.
Example IV.
Again, taking the same vessel, it is desired to find the effect
upon trim caused by consuming 200 tons of coal out of a cross
bunker. In this case we first assume in calculation that the
200 tons of coal are carried from the cross bunker and placed
vertically over the tipping centre, and the alteration to trim is
then found. Let the 200 tons be situated in a bunker 30 feet
forward of the tipping centre. The moment to alter trim 1 inch
we found in Example I. to be 651, and the moment to alter trim
is 200x30=6000.
— — - = 9 inches total change of trim.
651
Let it again be divided in the proportion of 8 to 7 = 5" and 4".
The draught will be 18' 0"-5" = 17' 7" forward, and 20' 0" +
4" = 20' 4" aft.
It is now assumed that the 200 tons weight is lifted from its
l)osition in the vertical line passing through the centre of gravity
of the waterplane, and got rid of (consumed). The draught
will be decreased uniformly all fore and aft. The " tons per inch "
is 30.
o'A = ^i" decrease in draught, and the ultimate draught is 17' 7" -
6f" = 17' OJ" forward, and 20' 4" - 6f" = 19' 9 J" aft.
Where a moderate quantity of cargo, or water in trimming tanks,
is discharged, the effect upon trim is found similarly to the method
given for consumption of bunker coal.*
For further illustrations and actual trim calculations see
Chapter X.
* With the aid of such diagrams as proposed, the efifect upon trim of
loading lar^e quantities of cargo, or other weight, producing considerable
increase in draught would be calculated in a very similar way.
1st. Find increase in draught parallel to present draught from displace-
ment scale.
2nd. Find position of centre of buoyancy of new layer of displacement
from curves of tipping centres.
3rd. Distribute cargo into intended positions in holds.
4th. Ascertain moment to alter the trim.
5th. Ascertain moment to alter trim 1 inch at this new load-Une, then
— r^ = Alteration of trim.
5th
TONNAOB. 239
CHAPTER VIII.
TONNAGE.
Contents. — Importance to Shipowners from an Economical Point of View —
Under Deck Tonnage — Gross Tonnage — Register Tonnage — Deductions
for Register Tonnage — Importance of Propelling Deduction in Steamers
— Deep Water Ballast Tanks — Deck Cargoes — ^Examples of Actual Ship
Tonnages — Sailing Vessels— Suez Canal Tonnage — Yacht Tonnage.
MERCHANT VBSSBLS.
Importance to Shipowners. — Ships' dues, such as pilotage,
dock, river, etc., are paid upon the register tonnage. Tonnage
is, therefore, a subject of great importance to the shipowner,
from an economical point of view. Nevertheless, considerable
misunderstanding is prevalent as to what tonnage really is.
Register tonnage does not, as some would imagine, give any
idea of the size of a vessel, for, an ordinarily proportioned vessel,
250 feet long, may have a register tonnage of 700, and another
of identical proportions may have a register tonnage of only 300,
and yet both vessels may have equal displacements. Thus we
gather that register tonnage gives no criterion of comparison
between one vessel and another as to their dimensions, displace-
ments, or deadweights.
A glance at a Board of Trade Certificate of Survey for any
vessel, or a Register of Shipping, shows three distinct tonnages,
viz. : — Under-deck, gross, and register. One ton of under-deck, or
gross tonnage, is equal to 100 cubic feet of capacity, so that these
tonnages may convey some idea of the entire internal capacity
of a vessel. Register tonnage, however, is a number having no
dependence upon the internal capacity as a whole, as already
stated, but is modified by the arrangement of the vessel, as
affected by the space occupied by the propelling machinery and
the crew, as well as other deductions allowed under the Merchant
Shipping Act of 1894.
Under-deck tonnage is the total tonnage up to the tonnage
deck, and is the first part of the vessel measured for tonnage.
Note. — The tonnage deck is the upper deck in all ships which have less
than three decks, and the second deck from below in all other ships.
240
KNOW YOUft OWN SHIP.
Under-deck tonnage is measured as follows : —
If the vessel is constructed with ordinary floors, the depth at any
part of the length of the vessel to the tonnage deck is measured
from the top of the floors, afterwards deducting the average thickness
of the ceiling, which is generally about 2 J inches, to one-third of the
camber of the beam, down at the centre of the beam (see fig. 132).
Should the vessel be built with a double bottom, the depth is
taken from the height previously described (fig. 133) down to the
plating forming the top of the double bottom where no ceiling
is laid ; or, where there is ceiling, the average thickness (usually
=1
BREADJTHS _|
Figs. 132, 133. — Under-Deck Tonnage ; Breadth and Depth.
about 2| inches) is deducted from this depth — no allowance what-
ever being made for grounds fitted between the tank top plating
and the coiling.
Where a vessel is constructed with ordinary floors at one part
of her length, and a double bottom at another, the tonnage in the
range of each part is computed separately, and the depths in each
part are measured as just described for vessels with ordinary floors
and double bottoms.
The tonnage measurements for breadths are taken from the
inside of the sparring in the hold, 2J inches being about the
usual thickness. Sometimes, instead of wood sparring, half
round iron is riveted to the reverse frames, especially in colliers.
In this case the breadths are taken from the half round iron,
side to side. Where neither sparring nor half roimd iron is
adopted, the breadths are taken to the reversed frames, or to the
inside of the framing.
The length for underKieck tonnage is measured from the points
at the extreme ends of the vessel where the inside lines of the
sparring unite, or in the case where no sparring of any sort is
fitted, to the points, where lines forming the inside of the framing
imitc (fig. 134).
The Board of Trade Surveyor then measures the inside of the
TONNAGE.
241
vessel to the positions indicated, and by means of Simpson's
Rules the cubic capacity in feet is found. If anything, this
method of finding the cubic contents by these rules, gives the
capacity rather under the actual, so that the diflFerence is slightly
in favour of the shipowner. In the case of vessels of the raised
quarter-deck type, the tonnage deck is the main deck, and where
_ _^ LENGTH FO R TO NNAGE
Fig. 134. — Length foe Undee-Deck Tonnage.
the main deck stops, and the raised quarter deck begins, the line
of the main deck is taken as the tonnage deck, as shown in
fig. 135, and the capacity of the raised quarter deck is computed
separately.
Gross Tonnage comprises the under-deck tonnage, together
with all enclosed erections in the form of poops, bridges, fore-
TONNAG& DECK
Fig. 135.— Tonnage Deck.
castles, spar decks, awning decks, raised quarter decks, deck
houses, engine and boiler casings,* etc. The chief exception to
this rule is that the crew's galley, crew's w.c.'s, and companions
are usually omitted in the calculations for tonnage.
By enclosed erections is meant spaces closed in on all sides ;
for example, poops with closed fronts of wood or iron, bridges
with closed ends, and forecastles with closed ends. Open-ended
* Engine and boiler casings form part of the gross tonnage, only, when,
under paragraph 78 of the Merchant Shipping Act of 1894, the owner desires
these spaces included in the calculation of the actual engine room.
Q
242 KNOW TOUR OWN SHIP.
poops, bridges, forecastles, or deck shelter, usiBd only for the
protection of passengers from the sea and weather, are not
included in the gross tonnage. Should, however, any houses
or storerooms of any kind be constructed beneath an open-
ended erection, they are reckoned in the gross tonnage.
Kegister Tonnage is obtained from the gross tonnage after
certain allowed deductions have been made, and as the various
dues and charges are levied upon this tonnage, the nature of the
deductions will form the subject of our next consideration. First
of all, it must be remembered that no deduction for any space
whatever is made, unless it be first included in the gross tonnage.
The deductions allowed, and the conditions required to ensure
the same, are as follows : —
1. Crew Space, — This must be available for the proper accom-
modation of the men who are to occupy it, protected from sea
and weather, properly ventilated and lighted; must contain
72 cubic feet and 12 square feet of floor room per man; must
be occupied exclusively by the crew and their personal property
in use during the voyage, and reasonable w.c.'s provided.
2. Master's Accommodation, — This space must be used exclu-
sively by him, and be reasonable in extent.
3. Engineers' and Officers' Accommodation. — This includes
berths, mess rooms, and reasonable w.c.'s used by them alone.
Note. — A mess room, used by both the captain and the officers, is not
deducted for register tonnage.
4. W.GJs. — In passenger steamers one w.c. for fifty passengers,
and not more than twelve w.c.'s altogether are allowed, but only
when situated above the tonnage deck.
5. Sail Room. — This refers to sailing ships only, and on
condition that the room does not exceed 2J per cent, of gross
tonnage. If it does exceed this percentage, 2^ per cent, only
of the gross tonnage is allowed.
6. Boatswain's Store. — 10 to 16 tons is about the usual allowance
for the average cargo steamer, varying according to the size of the
vessel.
7. Wheel Room, etc. — Space occupied exclusively for the
working of the helm, the capstan, the anchor gear, or for
keeping charts, signals, and other instruments of navigation.
8. Donkey boiler, when not connected with the engine room.
9. Deck shelter for passengers, when used only for this purpose,
and closed at the ends. A sketch of this space must be sub-
mitted to the Board of Trade, in order to obtain the approval
necessary for its exemption from the tonnage.
10. Propelling Deduciion. — The propeUing space includes
TONNAGE. 243
engine and boiler rooms, tunnel, donkey boiler space, if con-
nected with, and forming part of the main engine space, light,
and air space. This last comprises all space over or about
engines and boilers of reasonable extent, and used exclusively
for the admission of light and air;* it must also be safe and
seaworthy. Any such space admitting light and not air, or air
and not light, will not be included in the deduction. No stores
of any sort must be carried in the propelling space. Store rooms
or bunkers at the sides of the engines or the boilers will be ex-
cluded in making up this deduction. These restrictions being
fully complied with, paddle steamers with a propelling space of
from 20 to 30 per cent, of the gross tonnage will have an allow-
ance for propelling space of 37 per cent, of the gross tonnage.
Screw steamers with a propelling space of from 13 to 20 per cent,
of the gross tonnage will have an allowance for propelling space
of 32 per cent, of the gross tonnage. If the propelling space is
less than 20 per cent, in paddle vessels, and 13 per cent, in screw
vessels of the gross tonnage of the ship, the Board of Trade have
the option of either estimating the deduction at 37 per cent, in
the case of paddle vessels, and 32 per cent, in screw steamers of
the gross tonnage, or, if they think fit, allowing in the case of
paddle vessels, once and a-half the propelling space tonnage, and
once and three-quarters the propelling space in screw vessels.
The latter method is usually adopted.
When, however, the propelling space amoimts to 30 per cent,
or more of the gross tonnage in the case of paddle vessels, and
20 per cent, or more of the gross tonnage in the case of screw
steamers, the owner has the option »of having the deduction
estimated according to the 37 or 32 per cent, respectively, or, if
he desires, the deduction may be once and a-half the propelling
space in paddle vessels, and once and three-fourths the propelling
space in screw vessels. The question arises as to which of these
methods is more advantageous to the shipowner. Let us see.
Suppose a paddle vessel has a given gross tonnage of 100, and
a propelling space of 30 J tons. If the 37 per cent, method is
adopted, the deduction will be 37 tons. If the once and a-half
method is chosen, the deduction will be 30J+15J = 45f, which
is certainly preferable from an economical point of view to the
37 tons deduction. Again, let the gross tonnage of a screw
steamer be, say, 100, and the propelling space 20 J, which pro-
portion is not at all uncommon in vessels of average speed.
Choosing the deduction of one and three-fourths of the propelling
space, since the propelling space is over the 20 per cent., the
* Only light and air spaces above the upper deck are referred to here. (See
also footnote on page 241.)
244 KNOW TOUR OWN SHIP.
actual deduction would be If of 20J = 35|, which again is con-
siderably more preferable than 32 as a deduction, and thus when
we include the other deductions already enumerated, crew space,
etc., we can easily understand how, in some vessels of compara-
tively large dimensions, with largo propelling space, the register
tonnage is abnormally small. Take a fine high speed passenger
paddle steamer with a gross tonnage of, say, 100, and a large
propelling space (situated amidships, and occupying the bulkiest
part of the vessel) of, say, 40 tons of actual cubic measurement.
The deduction would be once and a-half of 40 = 60 for propelling
space, which without the other deductions is more than one-half
the gross tonnage. A similar screw steamer with a gross tonnage
of, say, 100, and propelling space by actual measurement of 30
tons would have a deduction of once and three-fourths of 30 = 62 J
for propelling space alone, also more than one-half of the gross
tonnage. These are by no means exaggerated examples. It
should be noted, that the higher the actual propelling space
tonnage is above the 30 per cent, of gross in paddle vessels, and
20 per cent, of gross in screw vessels, the greater is the proportion
of deduction.
In the ordinary tramp type of cargo steamers of comparatively
low speed, and where all available space is required for cargo and
bunkers, in many cases it might be found unwise to endeavour to
get a propelling space of 20 per cent, of the gross tonnage, as this
would require a sacrifice of too much space, which might be better
utilised for bunkers or cargo. In vessels of this type, to obtain
the 20 per cent, generally implies that it is only done by fitting
no side bunkers in engine or boiler space, or at most, small pockets.
However, this is a point needing the careful consideration of the
shipowner or designer of the vessel.
From the study of these deductions, it is evident that the Board
of Trade have given every encouragement to the providing of
suitable accommodation, or at least, reasonable berthing for officers,
and crew especially, for perhaps of all the comfortless and for-
bidding liuman habitations, the forecastles of some vessels would
claim a foremost place. We have also seen the advantage gained
by providing, when practicable, spacious and well-ventilated engine
and boiler rooms.
Before giving a few examples of the tonnage of actual vessels,
it may be well to point out one or two items from the Board of
Trade Tonnage Rules, which might be misunderstood.
In vessels constructed with double bottoms for water ballast,
the measurement for tonnage is only taken from the inner bottom,
plating (or ceiling), when the space between the inner and the
outer bottom, of tofiatever depth, is certified by a Board of Trade
TONNAGE. 245
Surveyor to be not available for the carriage of cargo, stores, or
fuel.
Deep Water Ballast Tanks. — Should, however, a vessel be
built with a raised platform in the bottom, or in other words, a
deep tank, thereby making it possible for cargo, stores, or fuel
being carried in this space, the depths for tonnage are taken down
through the platform, or the deep tank, to the height of the
ordinary floors, deducting the average thickness of ceiling (if
any).
Fore and after peak tanks, though constructed and intended
only for water ballast, are included in the measurement for
tonnage, unless, after submitting sketches to the Board of Trade
showing the construction, means of entering, and position of the
peak top plating in relation to the load waterline, exemption of
these spaces from the gross tonnage be granted.
Deck Cargo. — Ships engaged in the foreign trade, carrying
deck cargoes in the form of timber, etc., in spaces not included in
the measurement of the tonnage of the vessel, have the space
occupied by such cargo measured when the vessel arrives in port,
and the cubic capacity being computed, and divided by 100, gives
the tonnage which is deemed register tonnage, and charged upon
accordingly. Between the 31st of October and the 16th of April,
vessels from any port out of the United Kingdom are not allowed
to carry deck cargoes exceeding 3 feet in height above the deck,
under penalty.
Examples. —
Example I.
Steam screw collier, 228 feet long. Raised quarter-deck type.
Gross Tonnage —
Under-deck tonnage, 680
Erections —
Raised quarter deck, 60
Poop, t . . 47
Bridge 120
Lamp room under open forecastle, 5
Casings and deck houses on bridge,* .... 36
Excess of hatches over J per cent, of gross tonnage, . 16
Total 964
Propelling space, 210 = 21 "7 per cent, of gross tonnage, therefore the If
of actual propelling space is chosen.
1} of 210 = 367-5.
* It shotdd be understood that where the actual propelling space is over
13 per cent, and considerably less than 20 per cent, of uie gross tonnage, it
246 KNOW TOUR OWN SHIP.
Had the propelling space been less than 20 per cent, of the
gross tonnage the deduction would only have been 32 per cent.
of the gross tonnage = 308*4, which makes a diflFerence in the
ultimate register tonnage of 367*5 - 308*4 = 59*1. In tramp
vessels of this type it is not very usual for the propelling space
to exceed the 20 per cent, of gross tonnage. However, it will
be seen how spacious light and air space in the casings above the
tonnage deck will greatly assist towards this end. Sometimes
boiler casings are made wide enough for unshipping the boilers
without interfering with the deck.
The deductions for the register tonnage in this vessel were as
follows : —
Propelling space, . . . 367*5
Chart room, .... 5
Bridge accommodation for officers, 54
Crew space, .... 28
Boatswain's store, . .10
Total, . . 459*5
Gross tonnage, . 964
Total deductions, . 459*5
Register tonnage, . 504*5
EXAMPLB II.
Passenger steamer, 200 feet long, with a combined poop and
bridge, and a topgallant forecastle.
In vessels of this type, where a high speed is required, the
propelling space usually exceeds the 20 per cent, of gross tonnage
considerably, as seen by the following figures : —
Under-deck tonnage, .... 530
Poop, bridge, and forecastle, . 285
Deck houses and casings, ... 40
Gross tonnage, . . 855
Propelling space measured 235 tons = 27 per cent, of gross
tonnage.
The allowance, therefore, is If of 235 = 411 (32 per cent, of
gross = 273*6).
is unnecessary to include the light and air casings above the upper deck in
the tonnage. Sometimes where the actual propelling space is alightly less
than 13 per cent, of the gross the addition of the light and air casings or part
of these spaces may secure this percentage.
TONNAGE. 247
Deductions for register tonnage are as follows : —
Propelling space, . . . .411
Crew, 40
Passengers' w.c.'s, . . . . 4
Master's accommodation and chart room, 7
Boatswain's store, .... 10
Total. ... 472
Gross tonnage, . 855
Total deduction, . 472
Register tonnage, . 383
Example III.
Sailing-ship, 320 feet long, with a poop and a topgallant
forecastle.
Under-deck tonnage, .... 2900
Poop 110-5
Forecastle, 20*4
Houses on deck, . . . . 8'0
Gross tonnage, . . 3038*9
HA^
Deductions for register tonnage are as follows : —
Crew space, 115'9
Boatswain's store, .... 15
Chart house 4
Sail room, 20
Total, .... 154-9
Gross tonnage, . 3038 '9
Total deduction, . 154*9
Register tonnage, 2884
In sailing-vessels we always find the gross tonnage large as
compared with steamers. This is accounted for by the fact,
that there being no engines and boilers, and, therefore, no
propelling space deduction, the entire hold space is at the
disposal of cargo.
Suez Canal Tonnage. — For ships intended to navigate the
Suez Canal, a special tonnage certificate is required, since the
method of computing the nett register tonnage differs in a few
of its details from the ordinary system.
The extract given on the next page is taken from the Regulations
248 - KNOW TOUB OWN SHIP.
for the Namgation of the Canal, and may be of interest to those
unacquainted with the canal requirements : —
" When a ship intending to proceed through the canal shall have dropped
anchor either at Port Said or Port Thewfik, the captain must enter his snip
at the Transit Office and pay all dues for passage, and when there is occasion,
for pilotage, towing, and berthing ; a receipt for the same shall be delivered
to him, which will serve as a voucher whenever required.
" The following information must be handed in by the captain : —
** Name and nationality of the ship, to be identified by exnibiting the ship's
papers respective thereto.
** Name of the captain.
" Names of the owners and charterers.
**Port of sailing.
" Port of destination.
** Draft of water.
' ' Number of passengers as shown by the passage list. Statement of the crew
as shown by the muster roll and its schedules. (Sailors occasionally taken on
board of vessels passing through the Suez Canal are not considered as forming
part of the crew, and are taxed in conformity with the present regulations. )
'* Capacity of the ship according to the legal measurement ascertained by
producing the special canal certificate, or the ship's official papers established
in conformity with the Rules of the International Tonnage Commission,
assembled at Constantinople, in 1873."
Upon arrival at the canal the captain of every vessel receives a copy of the
ItegulatioTis,
The under-deck tonnage is measured, as shown in figs. 132,
133, 134, in the case of vessels constructed throughout with
ordinary floors or a cellular double bottom with horizontal top.
In vessels with a break or breaks or other irregularities in the
construction of the bottom, a slight difference arises owing to the
method of computation. Vessels with cellular double bottoms,
with the tank top rising from the fore and aft middle line to the
bilges, average about 3*5 per cent, less than the British for
imder-deck tonnage, owing also to a modification in the mode of
computation. In vessels built with Macintyre tanks, the depths
for tonnage are taken to the top of the inner bottom plating, as
in British. Under no circumstances are peak or any other tanks
exempted from the under-deck tonnage.
The gross tonnage includes, in addition to the under-deck
tonnage, every permanently-covered and closed-in space on or
above the tonnage deck without any exception. Such a space
as a shelter under a shade deck, open at the sides and supported
by means of stanchions, would, therefore, be excluded from the
gross tonnage.
The deductions for nett register tonnage are as follows : —
1. Propelling Space,
The owner has the option of either of the following methods : —
(a) The deduction may be one and three-fourths of the actual engine room
as measured for screw steamers, and one and a-half for paddle vessels ; o^,
TOKNAQfi. 24&
(b) The actual measurement of the engine room, together with the actual
measurement of the permanent bunkers.
Note 1. — Bunkers which are portable, or from which coal cannot be directly
trimmed into the engine room or stokehole, or into which any access can
be obtained otherwise than through the ordinary coal shoots on deck, and
from doors opening into the engine room or stokehole, are not included in
the measurement in paragraph {b). In no case, except in that of tugs, is
the actual engine room allowance to exceed 60 per cent, of the gross tonnage
of the ship.
Note 2. — Light and air spaces over the engines and boilers and above the
uppermost deck do not form a part of the actual engine room, except when
situated in a permanently-enclosed bridge space, poop, or other erection.
2. Crew spaces, exclusively and entirely occupied by the crew
and ship's officers, with the exception of the master, stewards,
cooks, passengers, servants, purser, clerk, etc., in short, only
such spaces are deducted as are occupied and used by those
persons engaged in the navigation and propulsion of the vessel,
with the exception of the doctor's cabin, when he is actually on
board and occupying such space. Also the covered and closed-in
spaces above the uppermost deck employed for working the ship.
Not more than 4 tons are allowed for an officers' and engineers' mess room.
For a second mess room for boatswain, carpenter, etc., not more than 2}
tons are allowed.
Should passengers be carried and no eating room be provided for them,
no deduction whatever is allowed for officers' and engineers' mess room.
When no passengers are carried, a bathroom, used entirely for the officers
and engineers, is reckoned as a deduction, and even when passengers are
on board, if there be more than one permanent bathroom, one of such spaces
is subject to deduction, being considered as specially for the use of officers
and engineers.
Not more than 2 tons are allowed for a bathroom.
3. TT.C's, exclusively for the use of the crew.
4. Wheel house, chart hovse, winch hcnise, look-out house.
Should the captain be lodged in the chart room, an allowance of 3 tons is
made for the space occupied by charts.
5. Cooking houses, used only for the crew. Passengers' galleys
are therefore not deducted from the gross tonnage.
6. A donkey boiler house in a closed space on the upper deck.
Should, however, the donkey boiler be used for hoisting cargo
no deduction is allowed.
In no case is the sum total of these deductions, with the excep-
tion of propelling space, to exceed 5 per cent, of the gross tonnage
of the ship.
No deduction is made for spaces used, or which may possibly
be used, for passengers' accommodation ; captain or passengers'
w.c.'s or lavatories, luggage storerooms, boatswain's store, or
sailroom.
250
KNOW tOUft OWN sHir.
In no case is any space to be deducted from the tonnage, which
is not first included in the gross tonnage.
YACHTS.
Yachts are measured for tonnage in exactly the same manner
as ordinary merchant vessels, the same deductions being allowed
for register tonnage.
For example, take a steam yacht 180 feet long. The gross
tonnage would be comprised as follows :
Under-deck tonnage, . . 520*5
Deck houses, ... 10
Monkey forecastle, . . 6*1
Total, . . 536*6
Deductions for register tonnage :
Propelling space, . . . 220*6
Crew space, . . . . 49'5
Master's room, . . . 3*5
■
Chart room, . . . 3*0
Boatswain's store, . . 3*2
Total, . . 279-8
Gross tonnage, .
Total deduction,
Register tonnage,
. 536*6
. 279*8
. 266*8
Measurement of Yachts for " Royal Thames " Yacht Club,
Measure the length of the yacht in a straight line at the deck
from the fore part of the stem to the after part of the stem
post. From this length deduct the extreme breadth. If the
vessel be iron or steel, this breadth is taken over the plating,
and if composite or wood, over the planking. The remainder is
the length for tonnage. If there be any projection of the stem
or stern posts beyond this length, such projection must be added
to the length already mentioned for tonnage purposes. Multiply
the tonnage length by the extreme breadth, then that product
by half the extreme breadth, and divide the result by 94. The
quotient will be the tonnage.
Example. — Steel yacht 200 feet extreme length over stem and stem posts
28 feet extreme breadth.
200 - 28 = 172 feet, length for tonnage.
172 X 28 X 14
94
= 7l7ff tonnage Thames measurement.
PBfiEfiOAHt). 2^1
CHAPTER IX.
FREEBOARD.
Contents. — Definition — Method of Computing Freeboard — Type of Vessel
— Nature of Deductions, and Additions to Freeboard — Examples of
Estimating Freeboard for Different Types of Vessels.
Definition. — B y the te rF> T^'^pphnr^vt^ in mpgyit the ^?^g^^ of. the
side of ^ «bifi^J;>ov^ the waterline . at ^ the middle of. her length,
measured from the top of the deck- at tha fiida. Should a wooden
deck be laid, it is taken from the top of the wooden deck. In
fig. 3, X shows the amoujit of freeboard, which, as will bo ob-
served, is 2 feet.
Buoyancy, Structural Strength, Stability, and Freeboard are
subjects closely related to each other ; indeed, the latter depends
almost entirely upon the other three. Hence the necessity, in
order to deal intelligently with freeboard, that the reader should
make himself acquainted with the contents of Chapters III. to
VI. inclusive.
Freeboard is given to a vessel as a margin for safety. For
instance, it would be possible for a ship to float with her deck
edge level with the water; but in such a condition, having no
reserve bouyancy she possesses no rising force, and would, there-
fore, be submerged beneath every wave, to say nothing, more-
over, of the possible effect of such a condition upon her stability.
The amount of freeboard for a particular vessel is modified by
the type, structural strength, erections on deck, sheer, camber,
etc. It must be borne in mind, however, as previously shown,
that such freeboard can only fully perform its chief function,
and be a real resource of safety, after a proper adjustment of
cargo has been carried out in the operation of loading. The
effect of freeboard on stability has already been dealt with in
Chapter VI.
Flush-decked steamers, other than spar- and awning-decked,
and equal in structural strength to 100 Al at Lloyd's, or equi-
valent strength at Bureau Veritas, or the British Corporation or
other classifying association, require from about 20 per cent, to
35 per cent, reserve buoyancy, according to their dimensions.
252
KNOW YOUB OWN SHIP.
This enables a vessel of suitable proportions to carry with safety
a deadweight for which her structural strength is adapted, and
to endure without damage the severe strains incurred when
among waves, already discussed in Chapter IV.
Therefore, all vessels below the standard of the one-, two-, and
three-deck type in structural strength, are compelled to carry a
smaller deadweight in proportion to their dimensions, with the
result that they have increased reserve buoyancy, and, conse-
quently, increased freeboard. Hence the spar-decked vessel, as
will be seen further on, requires a larger percentage of reserve
buoyancy than the one-, two-, and three-deck vessel; and the
awning-decked a larger percentage of total reserve buoyancy
Scale of Cubic Feet Capacity.
4COO
Fig. 136.— Cukve of Cubic Feet of Capacity.
than the spar-decked one, which results in both cases in
providing increased freeboard. Sailing-vessels require rather
more reserve buoyancy than steamers.
An examination of the Board of Trade Tables for such vessels
shows that this is the standard worked upon, the aim being to
give a freeboard such as will secure the stipulated amount of
reserve buoyancy, and thus give to vessels of suitable dimen-
sions sufficient strength for the total weight, including cargo, to
be carried, and the rising power and stability (when properly
loaded) requisite, when exposed to heavy weather, to ensure
safety.
Now, suppose we had a flush-decked vessel, classed 100 Al at
Lloyd's, to which we wished to assign a freeboard producing 20
FBBBBOABD. 253
per cent, reserve buoyancy. To find this accurately, it would
be necessary to construct a curve of capacity, identical in its
construction with a displacement curve, except that it shows
the whole external volume up to the deck, and instead of a scale
of tons at the top, the scale would represent cubic feet of
capacity.
Fig. 136 represents such a curve for a vessel 16 feet depth
moulded. It, therefore, comprises the total buoyancy of the
vessel up to the deck. This is found to be, say, 20,000 cubic
feet total buoyancy. 20 per cent, of 20,000 = 4000 cubic feet
to be left above the load waterline= reserve buoyancy.
20,000-4000 = 16,000 cubic feet from the keel to the load
waterline. This equals the vessel's load displacement, which
gives by the scale a draught of 14 feet, and a freeboard of 2 feet.
But, as is evident, this method entails considerable labour,
and would necessitate a copy of the vessel's lines being supplied
to the Board of Trade or Registration Society fixing the free-
board, and, therefore, in order to obviate this, another method
is adopted, which, though not strictly accurate, is sufl&ciently
correct for all practical and working purposes.
In the last chapter we saw how the Board of Trade Surveyor
measured the vessel for tonnage, and the results obtained provide
one of the principal factors in estimating the requisite freeboard.
In Chapter I. it was shown how coeflficients of fineness of
displacement were obtained, and in a similar manner a coefficient
of fineness is obtained from the tonnage under the upper deck,
and this, combined with the dimensions of the ship, as will be
explained, serves the same practical purpose, in referring to the
Freeboard Tables, as would the actual volume of the ship.
The coefficient of fineness is ascertained as follows : — For one-,
two-, and three-deck, and spar-decked vessels, divide 100 times
the total tonnage (1 ton measurement being 100 cubic feet)
below the upper deck (exclusive of any deductions) by the
product of the extreme length over the stem and the stem
posts on the load waterline, the extreme breadth over the
plating, and the depth of the hold.* In awning-decked vessels,
divide the tonnage to the main deck, by the product of the
length, the breadth, and the depth of the hold to the main
deck. In the case of vessels built with cellular double bottoms,
a modification or correction has to be made in estimating the
coefficient. It should, however, be remembered that the co-
efficient obtained is that of a vessel built with ordinary floors.
* The depth of hold used in ascertaining the coefficient of fineness is
taken to the top of the ceiling in iron and steel sailing-vessels, and to the
top of the floors in steamers.
254 KNOW YOUB OWN SHIP.
As an example, the tonnage under the upper deck of a certain
vessel is 78*4 ;
78-4 X 100 = 7840 cubic feet. The length is 100 feet,
The extreme breadth is 16 feet.
The depth of hold is 7 feet,
100 X 16 X 7 = 11,200.
^^^^ = 0-7 Coefficient of fineness.
11,200
and this coefficient is that used, in conjunction with the moulded
depth, to find the freeboard for this particular vessel from the
Tables.
The greater the depth of the vessel, the greater the freeboard.
The depth from which the freeboard, as ascertained by the
Tables, is measured, is the moulded depth, which is taken from
the top of the keel to the top of the upper deck beam at the
side, at the middle of the length. When a wooden deck of
extra thickness is fitted, the excess of thickness is added to
the moulded depth, and the freeboard taken upon this new
depth. Now, as wo have already pointed out, the structural
strength is a most important consideration in determining free-
board, the strongest ship with suitable proportions having the
least freeboard. The strongest vessel is the one-, two-, and three-
deck type, classed 100 Al at Lloyd's, or any other vessel, classed
or unclassed, but of equivalent strength. Next, we have the
spar-decked, and, lastly, the awning-decked vessel.
In assigning freeboard, the term "spar-decked vessel" applies
to all vessels equal to, or in excess of, the strength of Lloyd's
Spar-deck Rule, but do not reach the structural standard of
the three-deck requirements. The freeboard, therefore, depends
upon their strength. The standard height for a spar-deck is
7 feet ; therefore, since the freeboard is measured from the
spar-deck, it will be increased if the 'tween deck height is
more, and decreased if it is less than 7 feet.
In like manner, an awning-decked vessel is one equal to, or
exceeding Lloyd's structural requirements for awning-decked
vessels, but which does not reach the standard for the spar-deck
type. In this case also, the freeboard varies with the strength.
When the strength of the superstructure above the main deck
is less than is required by Lloyd's 100 Al Awning-deck Rule,
the freeboard is increased. The awning deck may, therefore, be
classed as simply an erection above the main deck, and since the,
freeboard is measured from the main deck, no modification is
necessary in respect to the height of the awning deck above the
main deck. The freeboard of awning-decked vessels classed
100 Al at Lloyd's is approximately one-twelfth the moulded
FBEEBOABD. 255
depth of the vessel less than would have been required had it
been built to the three-deck Rule, and flush decked.
No account is taken of erections above the awning deck of
vessels of this type. This also applies to spar-deck vessels with
but one exception. Since the longitudinal strains of vessels are
greatest in the region of amidships, it follows that any efficient
erection over this part of the length must add greatly to the
Strength. Such an erection receives full credit in assigning
freeboard in the three-decked heavy deadweight carrier. A
similar erection in the form of an efficient bridge on a spar-
decked vessel, extending over and protecting the engine and
boiler openings for at least two-fifths of the vessel's length, also
receives recognition on account of its addition to strength and
protection, though not in so great proportion £is in the three-
decked type. Thus such an erection on a spar-decked vessel of
20 feet moulded depth to main deck, merits a reduction of
3 inches on the freeboard.
For the sake of comparison, let us see the diflferences of free-
board in a vessel of each of these types — three-decked, spar-
decked, and awning-decked, classed 100 Al at Lloyd's. Let the
length in each case be, say, 300 feet, the coefficient of fineness '7,
and the depth to main, spar, and awning deck 25 feet, the spar
and awning deck each being 7 feet above the main deck.
The vessel of the first type would have a freeboard of 5 feet '
Oi inches.
The spar-decked would have a freeboard of 6 feet 2 inches.
The awning-decked would have a freeboard of 8 feet 7 J inches. >
r
For summer
voyages.
But even after the coefficient of fineness is found, there are
certain modifications to be carried out before the exact freeboard
is arrived at, and these modifications will next be dealt with.
Let it be understood that only vessels equal in strength to
Lloyd's 100 Al will be considered. Vessels below this standard
have increased freeboard : —
1. In spar-decked vessels, having iron-spar decks, and in
awning-decked vessels having iron main decks, the freeboard
required by the tables should be measured as if those decks were
wood-covered. Also, in vessels where j^^ths, or more, of the main
deck is covered by substantial enclosed erections, the freeboard
found from the tables should be measured amidships from a
wood deck, whether the deck be of wood or of iron. In apply-
ing this principle to vessels having shorter lengths of substantial
enclosed erections, the reduction in freeboard, in consideration
of its being measured from the iron deck, is to be regulated in
proportion to the length of the deck covered by such erectio
256 KNOW YOUR OWN SHIP.
Thus, in a vessel having erections covering ^^ths of the length, the
reduction is ^^^ths of 3^ inches (the thickness of the wood deck),
or 2 inches.
2. In flush-deck vessels of the one-, two-, and three-deck type,
and those of the same type with erections extending over less
than ^ths of the length, having iron upper decks not sheathed
with wood, the usual thickness of a wood deck is deducted from
the moulded depth of the vessel, and the freeboard taken from
the column in the tables corresponding with the diminished
depth. Thus, a vessel of this type with 19 feet 10 inches
moulded depth, with no laid wood deck, would be reckoned
as 19 feet 6 inches depth in the tables. Taking the coefficient
of fineness of this vessel at '7, referring to the freeboard tables,
the freeboard at 19 feet 10 inches depth would have been 3 feet
7^ inches, where, owing to the reduction of the depth to 19 feet
6 inches, the freeboard is 3 feet 6J inches. When the erections
in vessels of this type cover more than ^ths, and less than
^ths of the length, the correction for the wood deck is made
as explained towards the end of the previous paragraph.
3. Correction for Length, — The freeboard tables show that in
addition to the coefficient given with every depth, a fixed length
is assigned. For example, a vessel with a coefficient of 0*7, and
a depth of 16 feet, a length of 192 feet is assigned, but if the
length of our vessel with the same coefficient and depth be, say,
212 feet, a correction must be made for the additional 20 feet
of length. Wherever the standard length is exceeded, the free-
board is increased, and wherever it is less, the freeboard is
diminished. The greater the proportion of length to depth, the
greater the freeboard. The correction varies from about '7 to
1*7 inches for a change of 10 feet in length. In the case before
us, the correction is 1 inch per 10 feet, and thus for 20 feet it is
2 inches, which has to be added to the specified freeboard in the
table. Had the vessel been 10 feet less than 192, the freeboard
would have been reduced by 1 inch. The reason for this is
easily understood when we remember that the vessel with
greatest depth to length is the one most capable of resisting
longitudinal bending, and therefore best adapted to carry the
most deadweight. Where, however, steam-vessels with top-
gallant forecastles, having long poops or raised quarter decks
connected with bridge houses, the whole extending over -j^ths,
or more, of the length of the vessel, the correction for excess
of length should be half that specified in the tables ; so that if
the vessel we have taken as an example complied with these
conditions, the freeboard would only have been increased by
1 inch, simply because with so great a length of substantial
PRBBBOARD. 257
erections, the vessel has practically been increased in depth, and
consequently the proportion of depth to length is decreased.
The correction for length in spar-decked vessels varies from
about '9 to 1*5 inches per 10 feet, and for awning-decked vessels
from about '5 to '8 of an inch.
4. Sheer. — The Board of Trade Tables specify a mean sheer
for all types of vessels. Mean sheer is the sum of the sheers
at the ends of the vessel, or at whatever part of the length it
is specified, divided by 2 (see fig. 18).
Any increase in the mean sheer means an increase in the
reserve buoyancy, and exactly where it is much needed — viz.,
at the ends, giving additional rising power when the ship dips
into the trough of a sea, not to mention the increase of free-
board. This excess of buoyancy is recognised by the Board of
Trade, and a deduction allowed in the freeboard according to
the amount of the excess of sheer.
For all flush-decked vessels, the mean sheer is found by
dividing the length by 10, and adding 10 to the result Thus
a vessel 300 feet long will have a mean sheer of — — + 10 = 40
inches.
Flush-decked vessels of the one-, two-, and three-decked type,
with or without a short poop, a topgallant forecastle, and a
bridge house completely closed in at the ends, or a long poop,
or a raised quarter deck connected with an efficiently closed-in
bridge house, where the sheer is greater than in the Table, and
is of a gradual character, the reduction in freeboard is found by
dividing the difference between the actual sheer and the mean
sheer provided for in the Table, by 4. For example, a vessel 300
feet long, with a mean sheer of 46 inches, has a reduction in the
freeboard of ~ — = — = H inches. No allowance is given
to spar- and awning-decked vessels for excess of sheer; but in
any of these types, where the actual mean sheer is less than the
mean sheer by the rule, the difference divided by 4 gives the
increase of freeboard required for reduced reserved buoyancy.
Line 1 in the Table (p. 258) is for vessels having short poops or
forecastles only, or when, in addition, there is a bridge house,
with alleyways open at one or both ends. In these vessels the
important point is not the amount of sheer at the ends of the
vessel, for great additional buoyancy is given there already by
the erections, but over the length uncovered by substantial
erections. Therefore, in this particular case, the sheer is
measured at one-eighth the vessel's length from stem and stem.
One-fourth the difference between the sheer and the actual mean
258
KNOW YOUR OWN SHIP.
is approximately the amount of increase or decrease of freeboard,
as the case may be.
Length oyer which Sheeb is Measured.
100
150
200
260
300
350
400
Mean Sheer in Inches over the Length specified.
No. 1,
No. 2,
14
144
18
18i
22
23
26
27
30
31
34
35i
38
40
Line 2 in the Table is for vessels having short forecastles only,
and in this case the sheer is measured at points (1) one-eighth
from the stem, and (2), at the stern post, and correction for
additional sheer is made as in the previous case.
Note, — In flush-decked vessels, and in vessels having short poops and
forecastles, the excess of sheer for which an allowance is made is not more
than oue-half the total standard mean sheer for the size of the ship.
5. Round of Beam, — Th6 stipulated round of midship beam is
a quarter of an inch for every foot of the length of the mid-
ship beam. Here, again, any excess in the round of beam means
an increase of reserve buoyancy, and an allowance is made in the
freeboard. When the r'oimd of beam in flush-decked vessels is
greater or less than that given by the Kule, divide the diflference
in inches by 2, and diminish or increase the freeboard accordingly
by this amount.
Example. — The beam of a vessel is 40 feet, and the round of beam as
measured is 12 inches. This is 2 inches more than is required by the Kale,
therefore ^ = 1 = amount of decrease of freeboard. Where the deck is
partially covered with erections, the amount of the allowance for round of
beam depends upon the extent of the upper deck uncovered.
This rule for round of beam does not apply to spar- and awnmg-
decked vessels.
6. Corrections for Erections on Deck, — By erections on deck
is meant all closed-in or partially closed-in structures erected
above the upper deck of vessels built to the one-, two-, or three-
deck rule, — for example, bridges, poops, forecastle, raised quarter
decks, partial awning decks, etc., and also strong bridges in spar-
decked vessels covering the engine and boiler openings if such
erections extend over at least two-fifths of the vessel's length.
Now, erections such as those enumerated add greatly, according
to their proportions, to the reserve buoyancy, and, as in the case
of sheer and camber, the merits of the values of these erections
FBBBBOABD. 259
and additions to the reserve buoyancy and structural strength,
and the protection afforded to vulnerable localities such as deck
openings, are fully considered by the Board of Trade, and de-
ductions in the freeboard allowed accordingly. In assigning
allowances for erections, the complete awning deck is the standard
worked from.
As has already been pointed out, in taking out the freeboard
for a vessel with an aw^ning deck, the coefficient of fineness and
the depth are both taken to the main deck, and not to the awning
deck, and the freeboard is assigned and measured down from the
main deck. The awning deck thus comes to be what might be
termed a complete erection, extending all fore and aft, and
covering the main deck. All other erections partially covering
the vessel have their deductions on the freeboard made as a frac-
tional part of a percentage of the allowance for a complete awning
deck. The reader will easily see that a complete erection such as
an awning deck is always better than a partial one, comparing
length for length ; for instance, an erection covering three-
fourths of the vessel's length cannot be taken on equal merits
with three-fourths of the awning deck, since it is evident that
a well has been created on the weather deck in some part of the
vessel's length, forming a break in the longitudinal strength of
greater or less importance, and a means thus provided, to some
extent, for lodging seas on board, or the possibility created of
bulkheads being damaged, etc., therefore, three-fourths' erections
do not receive the same credit as three-fourths of the awning
deck, but a less fractional part. Again, the allowance varies
with the nature of the erections. This we shall endeavour to
show by arranging the erections according to their respective
values.
Taking a vessel 204 feet long, and, therefore, with an awning-
deck erection of the same length, we shall see what credit is
given, in assigning the freeboard according to the Board of Trade
Tables of Freeboard, for the various kinds of erections in
comparison with the allowance for the complete awning-deck
erection. This, it is hoped, will better enable the reader to
grasp the comparative values of the erections.
Let the moulded depth of the vessel be 17 feet, and the coefficient of
fineness '7.
The freeboard, had the vessel been flush -decked, to the two-deck rule would
have been 2 feet 10^ inches.
The freeboard, had the vessel been awning-decked, would have been 1 foot
4 inches.
2 feet lOJ inches - 1 foot 4 inches = 1 foot 6} inches = 18} inches,
this difference being the allowance for the complete awning-deck erection.
260 KNOW YOUR OWN SHIP.
Note, — For a raised quarter deck, 4 feet high, and connected with a bridge
house, covering the engine and boiler openings with an efficient bulkhead at
the fore end, the allowance is made as though it were a part of the actual
bridge, and equal in height. A decrease is made in the deduction, if the
raised quarter deck extends over the engine and boiler openings, or if it is
less than 4 feet high.
The deductions for erections are as follows : —
1. When the combined length of poop, or raised quarter deck,
connected with a bridge house covering in the engine and boiler
openings, and with an efficient bulkhead at the fore end, and top-
gallant forecastle is —
(a) y\ or '9 of the length of the vessel,
the deduction is *85 of the allowance for a complete awning deck.
Freeboard is ^Vtj" of 18^ inches = 15J inches.
(&) Y% or "8 of the length of the vessel,
the deduction is 75 of the allowance for awning deck. Freeboard is
yVv of ^^h inches = 13J inches,
(f) /^ or '7 of the length of the vessel,
the deduction is '63 of the allowance for awning deck. Freeboard is
iVtf of 18^ inches = 11| inches.
(d) T*iT or *6 of the length of the vessel,
the deduction is '5 of the allowance for awning deck. Freeboard is
^ji of 18| inches=9J inches.
These comprising the maximum reductions, it is essential that
the erections be of a most substantial character, the deck openings
effectually protected, the crew berthed in the bridge house, or
with satisfactory arrangements to enable them to get backward
and forward to their quarters, and sufficient clearing ports in the
bulwarks to speedily clear the deck of water. Vessels of this
type having no topgallant forecastle are allowed a less deduction
in the amount of freeboard than would otherwise be given for the
same length of erections. And if the bridge be a short one, in
front of, and only partially covering the engine and boiler open-
ings, again a less deduction is made. No allowance is granted for
a monkey forecastle which is less in height than the main or
topgallant rail.
Note 1. — A special allowance is made on the freeboard of vessels of the
foregoing or well-decked type when their erections extend over -^ of their
length, when their bridge bulkheads are specially strengthened, and when
the area of their water clearing ports in the bulwarks is at least 25 per cent,
in excess of the rule requirements. Such additional allowance must not
exceed 2 inches.
Note 2. — Special reductions in the freeboard may be obtained in strong
well-decked vessels of the modern type, having erections covering at least
Y^^ths of the length of the ship, the bridge house alone covering at least
^\ths of the length when extra strength is introduced, as given in section 44,
Lloyd's Rules for 1889, for iron and steel vessels. But, in no case most the
freeboards assigned to these vessels be less than would be assigned for a com-
plete awning deck.
FRBBBOARD. 261
2. In vessels with topgallant forecastles, short poops, and
bridge houses covering engines and boilers in steamers, with
efficient iron bulkheads at their ends, when the combined length
of erections is —
(a) -^ or '5 of the length of the vessel,
the deduction is '4 of the allowance for awning deck. Freeboard is
f of 18^ inches = 7i inches.
W Tn or '4 of the length of the vessel,
the deduction is *33 of the allowance for awning deck. Freeboard is
^ of 18^ inches = 6 J inches.
3. In vessels with topgallant forecastles and bridge houses only,
covering engines and boilers in steamers, with efficient iron bulk-
heads at the ends, when the combined length of erections is —
(a) -^ or "4 of the length of the vessel,
the deduction is '3 of the allowance for awning deck. Freeboard is
■^jj of 18^ inches = 5| inches.
{b) y% or '3 of the length of the vessel,
the deduction is '26 of the allowance for awning deck. Freeboard is
J of 18^ inches = 4f inches.
4. In vessels with only topgallant forecastles and poops, the
latter with an efficient bulkhead at the fore end, when the com-
bined length of erections is —
(a) f of the length of the vessel,
the deduction is ^ of the freeboard for the vessel flush decked. Free
board is ^i^^ of 34^ inches = 3^ inches.
{b) I of the length of the vessel,
the deduction is y^^ of the freeboard for the vessel flush decked.
Freeboard is ^hs of 34^ inches = 2J inches.
5. In vessels with topgallant forecastles only, the deduction
in freeboard is only one-half that prescribed in the previous para-
graph. Thus, were the erection ^ of the length of the vessel,
the deduction would be y^ of freeboard for the vessel flush
decked = If inches.
6. In vessels with poops only, the allowance is one-half that
for the previous paragraph (No. 5) for forecastles only of the
same length. Thus, did the length of the poop equal J erection,
the deduction would be y^ of freeboard for the vessel flush
decked = f inch.
7. In vessels with raised quarter decks only, not less than
4 feet high, the deduction is at the same rate as in the preceding
paragraph (No. 6).
8. In all vessels when the topgallant forecastle is not closed
at the after end by an efficient bulkhead, the length is never to
be estimated at a greater full value than ^ of the length of the
ship, but any extension beyond this may be estimated at one-
half the value. For example, a vessel 200 feet long has an
262 KNOW YOUR OWN SHIP.
open forecastle J of the length of the ship, or 50 feet ; its
value for deduction is 25 + 12|^ = 37J feet. When the top-
gallant forecastle has an efficient bulkhead with an elongation
abaft that bulkhead, the full allowance is given on the entire
length of the closed-in portion, and afterwards according to
the previous example.
9. When the poop has no bulkhead, one-half its length is
allowed for at the rate of a closed poop.
10. For bridge houses extending from side to side of the
vessel, when closed at the fore and open at the after end, with
all deck openings, doors, etc., properly protected, f of the length
is estimated as the value for deduction. When both ends of the
alleyways are open, one-half of the length is estimated as the
value for deduction.
Note* — Although it is possible to have occasional gales in the summer season
as severe as any in winter, yet it is quite unnecessary to remind anyone
acquainted with the sea that it is in the latter of these seasons that boisterous
weather is looked for. And thus in summer, when the danger from the
weather is decreased, there is no reason why a vessel should not be allowed,
to some extent, to carry more cargo than in winter. The Board of Trade,
therefore, allow a deduction from the winter freeboard for summer voyages,
amounting from 1 to 9 or more inches. Summer voyages from European and
Mediterranean ports are to be made from April to September inclusive. In
other parts of the world, the reduced freeboard should be used during the
corresponding or recognised summer months. Double the above reduction to
be allowed for voyages in the fine season in the Indian seas, between the
limits of Suez and Singapore. Vessels, up to and including 330 feet in length,
engaged in North Atlantic trades, are required to have an addition of 2 inches
to their freeboard, from October to March inclusive.
A few examples illustrating how the freeboard is ascertained
for diflferent types of vessels may be helpful in showing the
practical application of the freeboard rules, etc.
Let it be understood that by Tables A, B, C, and D is meant
the freeboard as specified by the Board of Trade for vessels of
various types.
Table A. — Flush-decked vessels of the one-, two-, and three-deck type.
Table B. — Spar-decked vessels.
Table C. — Awning-decked vessels.
Table D. — Sailing-ships.
Example I.
Flush-decked screw steamer, 300 feet long, 38 feet broad, and
21 feet depth moulded (no account is taken for any erection re-
quired for this vessel).
Sheer forward, 8 feet.
Sheer aft, 3 ,,
Coefficient of fineness, 0*8.
Wood deck on upper deck, 4 inches thick.
FtlBBBOABD. 263
Ft. In.
By Table A, for 21 feet depth moulded, the freeboard is, . . 4 3
Tne mean sheer, by rule, for a vessel 300 feet long is,
H^ + 10 = 40 inches!
10
In the example the vessel has 8 feet inches sheer forward,
and 3 , , „ sheer aft,
2) 11 „ „
5 ,, 6 ,, =66 inches mean
sheer,
which is an excess of 66 - 40 «= 26 inches (only half of
40* =» 20 inches is allowed), therefore,
20
— — 5 = reduction in freeboard, ... 5 .
4 '
The freeboard 4 feet 3 inches from Table A was for a vessel 252
feet long. A correction of 1 '2 feet per 10 feet of additional
length must now be made and added to the freeboard.
300 - 252 = 48
M X 1-2 - 676, about 5| inches, .
10 » * I
Winter freeboard from top of wood deck,
Deduct the thickness of the wood deck less the thickness of the
stringer plate (4 inch),
Less for summer.
3 10
5i
4
3i
3i
4
2}
3
91
Summer freeboard measured down from the top of the stringer \
plate at the side of the vessel at the middle of the length, j
Example II.
This vessel is identical in every respect with Example I.,
except that she has a raised quarter deck 4 feet high and 100
feet long, connected with a bridge house 80 feet long, with closed
ends, and a topgallant forecastle 30 feet long closed at the after
end. The upper deck is iron uncovered with wood.
These erections altogether measure 100 + 80 + 30 = 210 feet.
210 7
308 10
erections.
If we turn back to the remarks on Erections in this chapter
7
we find that — erections are allowed a reduction in the freeboard
equal to — - of the allowance for a complete awning deck.
* See Sheer,
264 KNOW YOUR OWN SHIP.
Ft. In.
By Table A, the freeboard of the vessel flush decked Is, . . 4 3.
The correction for additional sheer is, 6 J
3 8J
By Table C, for a depth of 21 feet, the freeboard is, . . . 2 2
(No account is taken of additional sheer in awniug-decked vessels.)
The allowance for a complete awning deck is, . . . . 1 6)
63 7
— — of 1 foot 6i inches = about 11 ^ inches = allowance for — - erections.
Now let us total up all the deductions.
1. Deduction for excess of sheer = 6^
2. Deduction for -^ erections = 11 i
3. Deduction for the thickness of a wood deck (less thickness of
stringer plate) when the upper deck is of iron, and covered by
— or more of substantial erections, 3^
10
Deductions, . . . . 1 9}
We have still to make the correction for excess of length.
—• X 1*2 = 6 '76. But only one-half of this should be taken,
10 ''
since the deck is covered by over — erections.
^ 10
6'76 -r 2 = 2*88 = 2i inches to be added to the freeboard, there-
fore the nett deduction will be 1 foot 9 J inches less 2| inches
= 1 foot 6| inches.
The freeboard by Table A is, 4 3
The deductions amount to, 1 6|
Winter freeboard, 2 8J
Less for summer, 2$
Summer freeboard measured down from the top of the
stringer plate at the side of the vessel at the
middle of the length, 2 5|
Example III.
This vessel has the same dimensions as Example I., with a
poop 50 feet long, a bridge house 60 feet long, and a topgallant
forecastle 40 feet long.
Iron upper deck uncovered with wood.
Coefficient of fineness = (3*8.
The bridge house is closed at the fore end with an eflBcient
bulkhead, but open at the aft^r end. Three-quarters of its length
will, therefore, be reckoned in\the erections. J of 60 = 45 feet.
FBBEBOAHD. 265
Total erections, 50 + 45 + 40 = 135.
135 4
300 = 10 «^««*^^^«-
The mean sheer at one-eighth the length from each end of
the vessel is 40 inches.
Ft. In.
By Table A, the freeboard is, 4 3
The mean sheer by the Rale is 30 inches.
40 - 30 = 10 excess of sheer, — = 2J redaction in freeboard, . 2^
4
4 OJ
Correction for length (added), 5f
4 6J
By Table C, the freeboard is, 2 2
Correction for length, at the rate of 0*6 foot per 10 feet, is
1? X 0-6;= 2| to be added, 2f
2 4|
By Table A, after corrections for sheer and length have been
made, the freeboard is, 4 6J
By Table C, after correction for length only has been made, the
freeboard is, 2 4f
Allowance for complete awning deck = 2 IJ
The redaction in freeboard for — erections is h of the allowance
10
for a complete awning deck = ^ of 2 feet 1} inches = 8^
inches.
By Table A, after the corrections for sheer and length have been
made, the freeboard is, 4 6J
Reduction for — erections, 8i
10 ' :
3 9|
Reduction for wood deck ^ of 3^ = 1^
Winter freeboard, 3 8J
Less for summer, 2|
Summer freeboard measured down from the top of the
stringer plate at the side of the vessel at the
middle of the length, 3 5|
Example IV.
Spar-decked steamer 260 feet long, 36 feet broad, and 24 feet
depth moulded.
Height of spar deck above main deck, 7 feet.
266 KNOW YOUR OWN SHIP.
Spar deck laid with wood deck 4 inches thick.
Coefficient of fineness = 0*8.
Depth moulded to main deck = 17 feet.
Ft. In.
By Table B, for 17 feet depth moulded, the freeboard is, . . 6 4 J
This is for a length of 288 feet. A correction must be made for
decrease in length at 1 inch per 10 feet, and subtracted from
the freeboard. .
288 - 260 = 28.
2? X 1 = 2-8 = about 2i inches, . . 2i
Winter freeboard from top of wood deck, .
Reduction for wood deck less thickness of stringer plate,
6
IS
81
6
lOJ
3
Winter freeboard,
Reduction for summer,
Summer freeboard measured down from the top of the
stringer plate at the side of the vessel at the
middle of the length, ^ 7^
Example V.
Awning-decked vessel 230 feet long, 32 feet broad, and 17 feet
depth, moulded to main deck.
Height from main deck to awning deck, 7 feet.
Coefficient of fineness, 0*8.
Mean sheer, 35 inches.
Iron awning deck.
Ft. In.
By Table C, for a depth of 17 feet, the freeboard is, . ' . . 6 li
230
The mean sheer by the Rule is — + 10 = 33, and this vessel
^ 10 '
having sheer in excess of the Rule, no correction is made.
This freeboard is for a vessel 204 feet long. A correction of
0*5 per 10 feet of additional length must be made, and
added to the freeboard.
230 - 204 = 26.
2? X 0-6 = li inches, .... \\
10 1
Deduction for thickness of wood deck less the thickness of
stringer plate when awning deck is of iron, ....
Winter freeboard,
Less for summer, ....
Summer freeboard measured down fr*
stringer plate at the side of
middle of the length,
PRSBBOARD. 267
Example VI.
Sailing-vessel 200 feet long, 34 feet broad, 19 feet deep.
Mean sheer, 40 inches.
Wood deck, 3 J inches thick.
Coefficient of fineness, 0*7.
Ft. In.
By Table D, for 19 feet depth the freeboard is, . . . . 3 10
The mean sheer by the Rule is — — + 10 = 30 inches.
40 - 30 = 10 inches excess of mean sheer.
— = 2J inches reduction in freeboard, . . 2J
4
3 7i
The length by the Rule for 19 feet depth is 190. A correction
must be made at the rate of 1*2 inches per 10 feet excess
of length, and added to the freeboard.
200 - 190 = 10 feet excess of length^
— X 1 '2 = about li inches to be added to the freeboard,
10
Freeboard from top of wood deck,
Deduction for thickness of wood deck less the thickness of stringer
plate,
Summer freeboard measured down from the top of the
stringer plate at the side of the vessel at the
middle of the length,
Note. — "Wherever definite rules have been quoted in the chapters on
Tonnage and Freeboard, it will be clearly understood that they have been
** extracted *' from the Board of Trade instructions to surveyors.
li
3
81
3
3
51
268 KNOW YOUB OWN SHIP,
TABLE OF NATDBAL SINES AND COTANGENTS.
Co- I De- De-
4-41S3
4-33U
4-2468
ia-0811
17-8105
16-3498
15-2570
u-sooe
7 ■5967
7-3478
7-1163
e-BBU
6-4971
6-3137
e-1402
5'9757
g™e. '■"Sl"^ ■^'""Bi^"'' gfii
3-605B
3'5457
3-4874
3'4308
2-9886
2-94fia
2-9042
27852
2-7474
2-7106
2-6746
2-4750
2-4443
2-4142
2-3847
1-6976
1-B808
1-6642
1-6479
1-4550
1-4*14
1-4281
Tablb op Natural Sink akj> Cotaitokntb [amlintad).
Do.
Blue.
Co-
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00-
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eree.
tongent.
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38
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270 KNOW TOUR OWN SHIP.
Table of N*TttBAL Sinib amd Cotasoests (amHitued).
lUent. gtet. eti
Coiina. TKngent
CALCULATIONS. 271
CHAPTER X. (Section I.)
CALCULATIONS.
Contents. — Useful Tables and Rules — Calculation of Weight of Steel Plate —
Solid Stanchion — Hollow Stanchion— Gallons in Fresh- Water Tank —
Tons in Coal Bunker — Rectangular Barge's Displacement and * * Tons per
Inch " Immersion — Simpson's Three Rules and Graphic Explanations —
Calculation of Area of Deck or Waterplane — "Tons per Inch" Immer-
sion of Ship's Waterplane — Ship's Displacement — Centre of Gravity of a
Waterplane, Longitudinally or Transversely — Centre of Buoyancy,
Vertically and Longitudinally — Moment of Inertia — Transverse Meta-
centre above Centre of Buoyancy — Centre of Gravity — Longitudinal
Metacentre above Centre of Buoyancy — Alteration of Trim — Area of
Section and Volume and Centre of Gravity of Wedge of Immersion or
Emersion — Centre of Effort,
USEFUL TABLES, RULES, AND PRELIMINARY
CALCULATIONS.
Useful Tables.
I cubic foot contains 6^ gallons.
1 ,, ,, of fresh water weighs 1000 ozs. or 62 J lbs.
1 „ „ of salt „ „ 1025 „ 64 „
In some localities, where the water is brackish, its weight per
cubic foot is between 1000 and 1025 ozs., and in other localities,
such as the Red Sea, a specific gravity of over 1*025 is found.
36 cubic feet of fresh water weigh 1 ton.
35 ,, ,, salt ,, ,, ,,
40 to 50 ,, ,, coal ,, ,,
1 ,, foot steel weighs 490 lbs.
1 ,, ,, wrought-iron ,, 480 „
1 ,, „ cast-iron ,, 454 ,,
Steel plates and bars are therefore about 2 per cent, heavier
than iron plates.
The thickness of steel plates is usually given in twentieths of an
inch, and the thickness of iron plates in sixteenths of an inch.
A square foot of steel plate 1 in. thick weighs 40 lbs. + 2%.
Therefore a square foot of steel plate ^ in. thick weighs 2 lbs. + 2%.
A square foot of iron plate 1 in. thick weighs 40 lbs.
Therefore a square foot of iron plate -^ in. thick weighs 2^ lbs.
272
KNOW TOUR OWN SHIP.
Timber-
cubic foot of elm
red pine
ft
>»
})
yt
ft
tt
it
n
112 lbs.
2240 „
20 cwts.
] 2 inches
3 feet
pitch pine
yellow pine
greenheart
lignum vitse
English oak
Riga oak
Dantzic oak
Indian teak
African teak
= 1 cwt.
= 1 ton.
= 1 ft
= 1 foot I
1 yard
))
tt
ft
weighs 84 lbs.
36
41
28
62J
83
52
43
47
55
61
tt
19
tt
it
it
»t
tf
Measurement of length.
144 square inches = 1 square foot |
9 ,, feet =1 ,, yard \
1728 cubic inches = 1 cubic foot )
= 1
ti
yard
it
it
it
ti
area.
volume.
it
cubic
>f
27 „ feet
Definitions —
Area is measurement in square yards, square feet, or square inches.
Volume ,, ,, cubic ,, cubic
Weight „ ,, tons, cwts., lbs., etc.
Circular Measure 1 degree = '01745.
Useful Rules.
To find the area of the following figures : —
I.
-VST
I
a
X.
L X B = area.
-- L --*i
II.
III.
W A ->!
— A >^
X
I
B >
Note. — Opposite sides parallel.
A X B = area.
Note. — Sides A and B parallel.
A + B ^
— t: — X C = area.
-B--*\
A X B
= area.
V.
D2 X 7854 = area.
CALCULATIOKS.
273
y.
Vl. To find circumference of a circle.
D X 3*1416 or D X 3f = circumference.
VII. To find the volume of an object, the length of which is
given, and the section of which is uniform throughout, the
section being like either I., II., III., IV., or V.
Rule — Multiply the area of the section (or one end) by the
length — the product gives the cubic contents.
To find the cubic contents of an object of b
the following elevation, the breadth being -*
constant throughout the length. 1*" ^
Find the area by Rule III. (B and b being parallel), and
multiply by the breadth.
—^ — X L X breadth = cubic contents.
VIII. To find the volume of a spherical object, the diameter D
being given.
D3 X -5236 = volume.
USEFUL RULES AND PRELIMINARY CALCULATIONS.
Example I.
Find the weight of a steel plcUe as per sketch, -^j^ thick, with
a circular hole, 2 feet diameter punched out.
5 + 3
— ^— X 6 = 24, area of plate 6 feet long.
4x5
= 10,
2 ' " "
2^ X '7854 = 3'1416 area of circular hole.
(24 + 10) - 3-1416 = 30-85 area of plate.
1 square foot ^ = 18 lbs. weight.
30-86 X 18 = 655-3 + 2 % = 555-3 + 11 = 566-3 lbs. weight.
Example II.
To find the weight of a solid iron standwm 20 feet long, 3
inches diameter.
3 inches = -25 of a foot.
•262 X -7864 X 20 X 480 = 471 '24 lbs. weight.
Example III.
To find the weight of a hollow iron stanchion 4 inches outside
diameter, 2 inches inside diameter, and 10 feet long.
The mean width of plate which would form this stanchion =
3 inches x 3-1416 = 9*42 inches.
Width. Thickness. ^^^^^
0-42 X 1 X (10 X 12) = 1130-4 cubic inches.
1130-4
1728
X 480 = 314 lbs. weight.
274 KNOW YOUR OWN SHIP.
Example IV.
To find the number of gallons and tons of fresh water a tank
will contain. The dimensions are: — Length, 12 feet; breadth, 6
feet; depth 7*3 feet.
12 X 6 X 7*3 = 525 '6 cubic feet in tank.
625*6 X 6 '25 (gallons in 1 cubic foot) = 3285 gallons contained in tank.
525*6
-_-- = 14*6 tons of water contained in tank.
36
Example V.
How many tons of coal zcill a coal bunher contain at 45 cubic
feet per ton ? It is 30 feet long, 10 feet broad, 13 feet deep.
30 X 10 X 13 „^ ^ ,
T^ = 86-6 tons.
45
Example VI.
Whai is the displacement of a rectangular barge 60 feet long,
20 feet beam, and 6 feet depth 1 It draws 4 feet aft, and 3 feet
6 inches forward in fresh water.
4-0 + 3*5 „ ^- J vx
5 = 375 mean draught.
60x20x375 .„- , ,. , .
5^ = 125 tons displacement.
Example VII.
The same barge in a light condition draws 1 foot fore and aft.
What weight or cargo is there on board ?
— = 33 '33 tons, displacement light.
Therefore 125 - 33*33 = 91*67 tons weight on board.
Example VIII.
How many tons would be required to increase the draught of this
barge 2 J inches ?
60 X 20 „.or: . . ,
2 '85 X 2*5 = 7*125 tons to increase draught 2 J inches.
Example IX.
What would be the increase in draught if 12 tons were placed on
board ?
12
^ „^ = 4*21 inches increase in draught.
2*85 °
Example X.
To find the area of such a figure as this, which is similar to
half of the deck of a ship or a h^ toaier^
^^\ plane. Such areas are found by what
^ 60' or- >-
^L A - kn'k. - - -- -J' are known as Simpson's Rules.
CALCULATIONS.
275
Simpson's First Rule. — ''Divide the hose into any even
number of eqtcal lengths" say 6, then ^ = 10 feet each length,
" through these points draw ordinates to the curve, which ordinates
toill consequently he odd in number," in this case, including the
endmost ordinates, there are 7. " Multiply the length of each
of the even ordinates by 4, and each of the odd ordinates by 2,
excepting the first and last, which multiply by 1. The sum of
these products multiplied by ^ of the common interval between the
ordinates will give the area required."
The calculation could be arranged in either of the following
ways {the 1th ord, in the diagram is supposed to be 1 foot) : —
No. of Ord.
Ord.
« 2
33
3-8
o
% 4
» 6
7-0
4-0
No. of
Ord.
14-8
Sum of even
ordinates.
29 '6 -f ^^^^^ ^^°^ ^^
\ even ordinates.
Q
O
Q
Q
o
1
3
5
7
•0 Half of Ist ord.
6*2
6-0
•5 Half of last ord.
4
5
6
7
Ord.
S.M.
0-0
1
3-8
4
6-2
2
7-0
4
6'0
2
4-0
4
10
1
Products or
Functions.
0-0
15-2
12-4
28-0
12-0
16-0
10
84*6 Sum ofpro-
ducts.
^ common interval V* -= 3*33
42*3 Sum of products obtained by
treating the ordinates by the
Multiplier for half Simpson's Multipliers.
Simpson's
whole Mul-
tipliers 2
84*8 Sum of products.
^ common
interval J^= 3 33
2538
2538
2538
281-718 Area.
This method is more
commonly adopted in
actual practice.
2538
2538
2538
281-718 Area.
276
KNOW YOUR OWN SHIP.
Simpson's Second Rule. — ''Divide the hose into equal
lengths, so that their number toill be a multiple of 3," in this case
(see figure) 6 lengths. " Through these points of division draw
ordinates to the curve, the total number of which, when divided by
3, gives a remainder of l,^* There are seven ordinates, |^ = 2, and
a remainder of 1. ** Call the ith (and if there had been more than
7 ordinates), the 7th, 10th, 13th, etc., ordinates, dividing ordinates,
and the others, excepting the first and last ordinates, intermediaie
ordinates. Add together the first and last ordinates, twice the
dividing ordinates, and three times the intermediate ordinates.
Multiply the sum by ^ of the common interval (10 feet), and the
product will be the area of the figure nearly.
The calculation is usually arranged as follows : —
No. of Ord.
Ord.
S.M.
Functions or Prodncts.
1
0-0
1
0-0
2
3-8
3
11-4
3
6-2
3
18-6
4
7-0
2
14-0
5
6-0
3
IS'O
6
4-0
3
12'0
7
1-0
1
0-0
f common interval = f of 10 =
74-0
375
1500
2625
277*50 Area.
It will be observed that the result is 4 square feet less than by
the 1st Kule. The latter is preferable when the number of
ordinates is such as to permit of the 1st Rule being applied.
Simpson's Third Rule is for finding the area of a part of a
.D figure such as shown in the adjoining diagram.
It is required to find the area of the part
C A E F {the 14 feet ordinate = GH),
^ ^ Let A E = 15 feet. Make E G = 15 feet also,
''^ /s'cC-^ /5'(f» "^ and draw G H to the curve.
Rule. — Add together five times the near end ordinate (A O) and
eight times the middle ordinate {EF), From the sum subtract the
far end ordinate {G H), and multiply the remainder by ^ of the
common interval. The product vyill give the area required.
CALCULATIONS.
277
The calculation is arranged as follows : —
8 X 5 = 40
12 X 8 = 96
136 sum.
Subtract 14
122 remainder.
5^5 common interval = f| = 1 '25
610
244
122
152 '50 area required.
Interval
Interval"^
By the following graphic method it is hoped that the applica-
tion of the foregoing Simpson's Rules will be more comprehensive.
First Rule. — Here is a figure, say, a piece of a ship's deck
A B is the fore and aft middle line, and
D C the curve of the deck. To find its
area by Simpson's First Rule, AB is
divided into two equal parts at the
point E, and E G is drawn to the curve.
By this rule, the first and last ordinates,
B C and A D, are always multiplied by
1, and the second ordinate (that is, the even ordinate) is multiplied
by 4. Then these products are multiplied by \ of the common
interval, that is, ^ of A E — E B.
Splitting this calculation up into its separate parts or steps in
the mode of procedure, we get : —
ADxiofA£ = area of A D J E.
EGx|rofAE = area of G E H F.
But this second ordinate G £, according to the rule, has to be multiplied
by 4.
. '• 4 (E G X ^ of A E or E B) = area of the 4 rectangles contained in
OKLS.
Then, finally, BCx|ofEB = area of L B C M.
The sum of these three parts gives the area of the whole figure A B G D.
It will be noticed in this calculation that a piece of the area of
the curve is lost over the rectangle A D J K, but a piece is gained
within the rectangle at the other extremity M L B C. Similarly,
a piece of the area of the curve is lost over the two rectangles
GELS, and a piece gained within th^ rectangles K E G,
278
KNOW YOUR OWN SHIP.
The areas of the two pieces gained and the two pieces lost
approximately balance each other.
While this rule approaches very nearly to the truth, it is not
absolutely correct. However, for all practical purposes, and in all
ship calculations, when the rule is carefully applied, the error is
so slight as to be unnoteworthy.
Where a figure is divided into a considerable even number of
equal spaces, the rule applies in exactly the same manner as just
described. For the first two spaces the multipliers are 1, 4, 1,
and for the second two spaces the multipliers are 1, 4, 1, and so
on.
1
1
1
1
1
1
142424241
To give a practical example illustrating what has been explained, let
A B = 18 feet, A D = 4 feet, E G = 6 feet, and B C = 7 feet The common
interval between ordinates = -i^ = 9 feet, and one-third of the common
interval = 3 feet.
4x3
4(6 X 3)
7x3
12, area of A D J K.
72 ,, the four rectangles contained in E L S,
21 .. L B C M.
105
f»
If
whole figure.
Arranged in the usual form, and as previously described.
No. of Ord.
Ord.
S. M.
Products.
1
2
3
4
6
7
1
4
1
4
24
7
J common interval = f =
35
3
105 Area of whole figure.
Simpson's Second Rule. — With the explanatory notes upon
Simpson's First Rule, the reader will be able to follow the graphic
explanation here given for Simpson's Second Rule.
Simpson's Multipliers are 1, 3, 3, 1, making altogether 8 oblongs
and 3 intervals. 1 oblong is as long as the first ordinate^ 3 $U9
CALCULATIOKS. 279
long as the second ordinate, 3 aa long as the third ordinate, and I
( the part of the figure the
Wwtt
Simpson's Third Rule. — C DAB
area of which is foimd
by this rule.
Simpson's Multipliers
are 5, 8, and 1, which
latter product haa to be
deducted. There are,
therefore, 6 + 8 - I =
12 oblongs, 5 of them
are of the length of the
ordinate AD, 8 of the
length of the ordinate
B C, which includes 1
oblong more than the ' ""
required number to cover the area ADCB. The \
Delect the black wedge at their upper extremities, while the
8 oblongs gain a wedge outside the curve. By deducting the last
ordinate E F, the surplus oblong to the right of B C is corrected,
while the excess in length of the ordinate E F over B C produces
an area indicated by a black oblong, which together with the
lost wedge over the first 5 oblongs approximately neutralises the
excessive area obtained over the next 7 oblongs. The width of
on oblong is y'^ of the tehole intei-val.
A study of the foregoing diagrams, showing the application of
Simpson's Rules, indicates clearly that the nearer the ordinatea are
spaced to each other, or, in other words, the more intervals into
which an area ia divided, the nearer does the calculation approach
to accuracy. Supposing the area of a ship's deck, 200 feet long,
be divided into 1 2 interi'als, a stiidy of these rules will further
show that, while they apply with great accuracy to the middle
280
KNOW TOUR OWN SHIP.
f length or more, the sudden curve of the ends of the deck towards
the stem and stem, especially in a bluff cargo vessel, renders
the calculation far from even approximately accurate for these end
areas.
Let the adjoining figure represent the after 33*33 feet of this deck,
covering exactly 2
intervals. The
black wedges in-
dicate the area
within the deck
line which is in-
cluded by the rule,
and the hatched
areas indicate the area outside the deck line which is gained by the
calculation. The inadaptability of the rule, as previously given,
to apply to such an area as this, with any degree of accuracy,
is obvious. But by a modification in the application of the
rule itself, this inaccuracy can be largely obviated.
As previously stated, the closer the ordinates are spaced, the
greater the degree of accuracy obtained. By this process of ap-
'^ 'l$gg ^2- iB-ee *"'
2 half 1%
-interra} — tep*-
whole 4!
t'n terra/
plication of the first rule, the first interval is subdivided, and
an ordinate measured at the point of division. Simpson's
Multipliers now become half of what they were originally, viz.,
J, 2, ^. In other respects the calculation is carried out in the
usual manner. Simpson's Multipliers are now : —
J 2 i (See accompanying
14 1 diagrams).
i 2 li 4 1
By this method of subdivision of the intervals the discrepancy
between the excess and loss of area of the deck is reduced, and
by means of a still further subdivision the error can be lessened.
CALCULATIONS.
281
Example 11.
To Calculate an Area by Introducing Subdivided Intervals. — The
half ordinates for a ship's waterplane at, say, the load line, are
2, 8,* 12, 14, 16, 17, 16-6, 15, 11, 7,* 0, ordinates 8 and 7 being
subordinates (half-ordinate means ordinate for half width of water-
plane). The common interval is 18 feet. Find area of whole
waterplane.
No. of Ord.
i Ord.
S. M.
Products,
1
2
i
1
14
8*
2
16
2
12
14
18
3
14
4
56
4
16
2
32
5
17
4
68
6
16-6
2
33*2
7
15
4
60
8
11
14
16-5
H
7*
2
14
9
4
314-7
J common interval = ^ = 6
Area of half waterplane 1888 '2
Multiplier for both sides 2
Area of whole waterplane 3776*4
Example 12.
To Find the " Tons per Inch " Immersion of the Foregoing Vessel
3776*4
at the Load Line, tstt- = 8*99 " tons per inch " immersion.
420
By means of Simpson's Rules, the area of any waterplane, deck,
or transverse section of the hull of a ship is easily found, whatever
may be the number of intervals into which these areas may be
divided.
In such an example as that shown by the figure, where there are
eleven intervals, neither
the First nor the Second
Rule will apply for the
whole length, but then, by / 2 i"
making use of the Third
Rule, the area can be found. Thus, by using the First Rule, the
area of the whole figure up to the 1 1th ordinate can be found,
and by using the Third Rule the area of the last space between
282
KNOW YOUR OWN SHIP.
the 11th and 12th ordinates is found. The sum of the two
parts gives the whole area.
Example 13.
BO
20-2
Shotos a further Application of
Simpson's Rules in ascertaining
the Capacity of a Cross Bunker. —
The bunker is 20 feet long and of
constant section throughout its
length. The ordinates of the
transverse section are shown upon
the sketch. Find the quantity of
coal it [will contain at 45 cubic
feet per ton. The bottom interval
is subdivided.
No. of Ord.
Ord.
S. M.
Products.
1
20
1
20
2
20 '2
4
80-8
3
20-4
2
40-8
4
20-4
4
81-6
5
20-1
H
30-15
H
18-0
2
36-00
6
16-0
h
8
297-35
J of common interval = J of 3 = 1
297-35
Multiplier for both sides 2
Area for both sides
594-7
20 Length of banker.
45)11894 Cubic feet in bunker.
264-31 Tons in bunker.
We have shown how Simpson's Rules may be applied to find
the area of a deck, a waterplane, or a transverse section of a ship.
In a similar manner, these rules may be used to find the dis-
placement of a ship floating at a given waterline.
CALCULATIONS.
283
Example 14.
To Calculate a Ship's Displacement^ \st Method, — She draws
20 feet of water from the top of the heel. Divide this depth
into a number of equal intervals, suitable for the application
of Simpson's First or Second Rule, say, five equal intervals, each
being 4 feet, with the bottom interval subdivided. The area
of each of these waterplanes is now calculated as previously
shown.
Let the total area of
No. 1 = 20,000 !
square feet.
„ 2 = 19,500
i» -
„ 3 = 18,000
„ 4 =14,000
„ 5 = 8,000
,, 5^ = 4,000
„ 6 = 1,000
«
T —
'1 « I
These areas are treated by Simpson's Multipliers ; the sum of
the products multiplied by J of the common interval (when the
First Rule is applied) equals cubic feet displacement, and in a
similar manner the Second Rule may be applied when the intervals
are suitable.
No. of Area.
Area.
S. M.
Products.
1
20,000
1
20,000
2
19,500
4
78,000
3
18,000
2
36,000
4
14,000
4
56,000
5
8,000
H
12,000
H
4,000
2
8,000
6
1,000
*
500
Common interval
210,500
4
Divide by 3 for J common interval 3)842,000
35)280,666 Cubic feet displacement
8,019 Tons displacement.
"^^^^^^^
284
KNOW TOUR OWN SHIP.
Example 15.
To Calculate a Ship^s Displacement, 2nd Method, — Another
method of finding the displacement is to divide the length
of the vessel into a number of equal intervals suitable for
the application of Simpson's Rules. The areas of the transverse
sections up to the load waterplane are calculated at each of these
stations, and these areas are put through Simpson's Multipliers,
and the calculation carried out in a way exactly similar to the
foregoing examples.
A vessel, 200 feet long, is divided into twelve intervals, and the
areas are calculated at each station. The areas are as follows : —
6, 200, 280, 350, 400, 400, 390, 370, 330, 280, 240, 180, 18.
The common interval between the areas is — -^ .= 16*66 feet.
12
No. of
Section.
Area.
S. M.
Products.
1
5
1
5
2
200
3
600
3
280
3
840
4
350
2
700
5
400
3
1200
6
400
3
1200
7
390
2
780
8
370
3
1110
9
330
3
990
10
280
2
560
11
240
3
720
12
180
3
540
13
18
1
18
I of 16-66 =
9263
6-24
35)57801*12 Cubic feet displacement
1651-46 Tons.
ExAMPLB 16.
To Find the Centre of Gravity of a Waterplane or of a Transverse
Section of a VesseVs Displacement. — In Chapter II., it has been
shown how to find the centre of gravity of a number of weights
ranged along a bar, from a given point. The principle holds good
in all other calculations for centres of gravity.
Let the adjoining figure represent a ship's deck, the area of
which is required. The lengths of the half-ordinates are shown on
the diagram, and the intervals between the ordinates. Had 1,
CALCULATIONS.
285
10, 12, 8, been weights upon the deck the centre of gravity of
these weights only would have been found by multiplying each by
its distance or leverage from one end of the deck, and dividing the
sum of the moments obtained by the simi of the weights. How-
ever, though the ordinates are not weights, they serve the same
purpose as weights, being ^
representative of where ^ — ^T^g..^
the areas are greatest and ^y^ ^I ^i
least. But just as in
calculating the area of a deck, Simpson's Rules are applied in
order to obtain greater accuracy than would be obtained by
simply taking the mean of all the ordinates, in like manner, in
obtaining the centre of gravity of the deck we employ Simpson's
Rules, and thereby, greater accuracy is obtained by using the
ordinates multiplied by their respective multipliers as indices of
the fulness or fineness of the deck, than by using the ordinates
themselves. The calculation would be done as follows : —
No. of Ords.
iOrds.
S. M.
Products.
Leverages.
Moments.
1
1
1
1
2
10
4
40
6
240
3
12
2
24
12
288
4
8
4
32
18
576
5
1
24
1104
97
97
= 11-38
1104
The centre of gravity of the deck is 11*38 feet from the left-
hand endmost ordinate. In practice, it is usual to use only the
number of intervals for leverages, and multiply the sum of the
moments so obtained by the interval. This effects a saving in
figures. By this method the calculation would be as follows : —
No. of Ords.
i Ords.
S. M.
Products.
Leverages.
Moments.
1
1
1
1
2
10
4
40
1
40
3
12
2
24
2
48
4
8
4
32
3
96
5
1
4
184x6
97
97
= 11*38 C. G. from first ordinate.
184
286
KNOW YOUR OWN SHIP.
Example 17.
To Find the Perpendicvlar Centre of Gravity of a Half
Waterplane Transversely from the Fore and Aft Centre Line, — Rule.
— Take the half squares of the ordinates, and treat them by
Simpson's Multipliers as though they were the ordinates for a new
curve. The area of this hypothetical curve is the moment of the
figure relatively to the fore and aft centre line. Divide this
moment by the actual area of the half waterplane, and the result
is the perpendicular distance of its centre of gravity from the
longitudinal middle line of the waterplane.
The following example will serve as an illustration, the common
interval between the ordinates being 18 feet : —
No. of
Ord.
1
2
8
4
5
Ords.
S. M.
Products.
2
1
2
. 5
4
20
8
2
16
4
4
16
1
Squares of
Ordinates.
4
25
64
16
Products of Squares
of Ordinates.
4
100
128
64
54
^ of common interval ■= Jj^ 6
824
i squares 2)296
148
^ common interval 6
moment 888
888 _ n.-A — Perpendicular distance of centre of gravity from
^^ _ J / 4 — longitudinal centre line.
Example 18.
To Find the Centre of Buoyancy or Centre of Gravity ofDutplace'
ment. — Suppose, first, that it is desired to obtain the height of the
centre of buoyancy above the keel.
The draught (measuring from the top of keel) is divided into a
number of equal spaces in exactly the sam^e way as is done for
displacement. The area of each of these waterplanes is calculated
by the application of one of Simpson's Rules. These areas of
waterplanes are then put through Simpson's Multipliers. Thus
CALCULATIONS.
287
far the calculation has resembled that for displacement. All this
information may, therefore, be copied direct from the displacement
calculation, or the displacement calculation itself may be used, as
is generally done in practice. If the centre of buoyancy is
required from the top of the keel, the products of areas are
multiplied by their respective leverages from the top of the
keel. The sum of these moments divided by the sum of the
products of areas will give the height of the centre of buoyancy
above the top of the keel. The steps in this calculation are
identical with those followed in the previous example for finding
the centre of gravity of a waterplane, the areas of the horizontal
waterplanes taking the place of the ordinates of the waterplane.
As an example, suppose it is required to find the centre of
buoyancy above the keel of the vessel whose displacement was
found in Example 14.
No. of
Horizontal
Area.
S. M.
Products.
Leverages.
Moments.
Area.
1
20,000
1
20,000
5
100,000
2
19,500
4
78,000
4
312,000
3
18,000
2
36,000
3
108,000
4
14,000
4
56,000
2
112,000
5
8,000
li
12,000
1
12,000
54
4,000
2
8,000
i
4,000
6
1,000
i
600
000
210,500
Common interval
648,000
210,500)2,592,000
Centre of buoyancy above top of keel = 12*3 feet.
Example 19.
To find the fore and aft centre of bvxyyancy the same method
exactly is adopted, using vertical areas.
As an example, find the centre of buoyancy of the vessel in
Example 15.
KNOW TODS OWN SHIP.
No. of
Vwt. Area.
Area.
S. M.
ProdnctB.
Leverages.
Momento.
1
2
5
200
1
5
eoo
600
280
810
1880
350
2
700
2100
6
400
a
1200
4800
6
400
s
1200
8000
7
390
780
4880
370
3
1110
7770
330
990
7920
10
280
2
MO
eo4o
11
240
3
720
10
7200
12
180
3
510
11
6940
13
IS
1
IS
12
218
g283)seS,740-86
Centre of buoyancy from area 1 97'02 feet
EXAUFLE 20.
To find the momeni of ittertia of a waterplane (required in
order to arrive at the height of the transverse metaceotre above
the centre of buoyancy), relatively to the fore and aft axle pass-
ing through the centre of gravity
of the waterplane. Imagine tbe
waterplane to be divided into an
infinitely small number of units of
area. Multiply each one of these
units of area by the square of its
distance from the fore and aft centre
line of the waterplane, which is the
axis about which the moment of
inertia is calculated. The sum of
all these products is the moment of
inertia required. Let theadjoining
figure serve as an illustration. Here
^ we have, say, a midship portion of
the area of a waterplane. It is 6
feet long and 9 feet wide, that is, 41
feet on each side of the fore and aft middle line. Let it be divided
into unite of area of 1 square foot each,
Multiply each of these areas by the squares of their reepeotave
distances from the axis, as follows ; —
,-
-
—
srf_
1
1
ft^s
11
'
1
1
1
i
CALCULATIONS.
6(
6<
61
6(
6<
:-5 X -252) =
[ 1 X 12) =
: 1 X 22) =
: 1 X 32) =
[ I X 42) =
•1875
6 0000
24-0000
54-0000
96-0000
289
180*1875 Moment of inertia for one half of plane.
2 Multiplier for both halves.
360*3750 Total moment of inertia.
The moment of inertia is first obtained for the half waterplane
relatively to the fore and aft axis of the plane, as in the foregoing
case, and the result is multiplied by 2 for the whole plane — the
other half being exactly similar when the vessel is upright.
Thus, on one side, we have : —
6 half units of area at a distance of *25 of a foot,
then 6 „ ,, ,, 1 foot
„ 6 ff „ „ 2 feet, and so on.
Naturally, as our units of area are not infinitesimally small, the
result can only be approximate. The smaller the units of area,
and therefore the greater number of them, the more correct is the
result. It will be obvious that such a method as this could not
be applied to such a huge area as a ship's waterplane.
Rule for Moment of Inertia of a Ship^s Waterplane : —
Divide the fore and aft axis into a nimiber of equal intervals
suitable for the application of one of Simpson's Rules. Measure
the half ordinates at the points of division, and cube each of them.
Take one-third of these cubes, and deal with them as though they
were ordinates of a curve, the area of which has to be found.
Such area would be the moment of inertia of the half waterplane.
The moment of inertia of the foregoing figure found by this
method would be as follows : —
i Ords.
Cubes.
S. M.
Products.
4-5
4-5
4-5
91*125
91-125
91-125
1
4
1
91-125
364-500
91-125
i of cubes 3)546-750
I common interval = | =
182-25
1
1 82 '25 Moment of inertia for half plane.
2 Multiplier for both halves.
364*5 Total moment of inertia.
290
KNOW TOUR OWN SHIP.
It is now seen that the previous method was only approximate,
being over 4 less than the correct calculation gives.
In an earlier chapter, we have shown that the moment of
inertia of a rectangular waterplane is: —
Length of waterplane x Breadth*
12
therefore, applying this to the same figure
6 X 9»
12
= 364-5,
which result is similar to that of the last calculation.
Calculation for Moment of Inertia of aa Actual Ship's Water-
plane. — To find the moment of inertia of the load waterplane of a
vessel whose half ordinates are 0, 2*5, 6, 9, 11, 12, 10, 7, 5, 2, *5.
The common interval between the ordinates is 9 feet.
No. of
Ord.
J Ords.
Cubes of i
Ords.
S. M.
Moments.
1
•0
•00
1
•00
2
2-5
15-62
4
62-48
3
6-0
216-00
2
432-00
i
4
9-0
729-00
4
2916-00
5
11-0
1331-00
2
2662-00
6
12-0
1728-00
4
6912-00
7
10-0
1000-00
2
2000-00
8
7-0
343-00
4
1372-00
9
5-0
125-00
2
250-00
10
2-0
8-00
4
32-00
11
•5
-12
1
-12
i of cubes 3)16,638-60
^ common interval = ) =
5546-2
3
16,638-6 M of 1 of i^ plane.
For both halves of waterplane 2
33,277 '2 Moment of inertia.
Example 21.
To Find the Height of Metacentre above the Centre of Buoy-
ancy : —
Moment of inertia of waterplane ^ ^^^.^^^re above centre of buoyancy.
Displacemeut m cubic feet
CALCULATIONS. 291
As an example, suppose the moment of inertia of the foregoing
example is for a vessel of 300 tons displacement at load draught.
The height of metacentre above centre of buoyancy would be : —
33,277 ^S_3^_
300 X 35"10,500"^^^^®®^-
Example 22.
To Find the Position of the Centre of Gravity of a Vessel in
Relation to the Metacentre, by Experiment. — This has been
dealt with, and an example worked out in Chapter VI. (Section
I.), page 128.
Let W = weight moved across deck.
d = distance weight is moved;
D = displacement in tons.
W x d
— y: — = G G' (shift of centre of gravity transversely).
G G' X cotangent of angle of keel = G M (metacentric height).
^ . e 1 length of plumb line in inches
Cotangent of angle = ," . .. ^ ^ , r^p = — -. — ^t-
° ° mean deviation of plumb line in inches.
^V X d length of plumb line in in ches _ p » r
D mean deviation of plamb line in inches"
Example 23.
To Find the Centre of Gravity of a Ship by Finding the Distance
of the Centre of the Weight from^ say, the Bottom of the Keel. —
Multiply every item of weight in the ship by its distance above
the bottom of the keel. The sum of all these products or
moments divided by the sum of all the weights (the total of
which equals the total weight of the ship), gives the height of
the centre of. gravity above the bottom of the keel.
Example 24.
To Find the Height of the Longitudinal Metacentre above the
Centre of Buoyancy. — The principle of this calculation is identical
with that alreaxly given for height of transverse metacentre above
centre of buoyancy.
The moment of inertia of the waterplane is found relatively to
a transverse axis passing through the centre (centre of gravity)
of the particular waterplane. When this moment of inertia is
292 KNOW TOUR OWN SHIP.
found, and divided by the displacement in cubic feet, the result
is the height of the longitudinal metacentre above the centre of
buoyancy.
Here, again, the moment of inertia is the sum of the products
of each of the units of area in the waterplane, multiplied by the
square of their respective distances from the transverse axis.
Were the waterplane rectangular, the moment of inertia would be
found by identically the same method as in the first two calcula-
tions in Example 20, excepting that what was in that case the
length now becomes breadth, and the breadth becomes length.
Breadth x Length' 9x6' - ^„ i. * • _x-
r^r — = — — — = 162 moment of inertia.
Owing, however, to the shape of an actual ship's waterplane, a
modification in the application of the rule is necessary.
The method adopted is as follows : —
let. Find the Moment of Inertia of the Waterplane, Relatively to
One End of the Waterplane, — Rule, Divide the fore and aft middle
line into a number of equal intervals suitable for the application of
one of yimpson's Rules. Through these points draw ordinates to the
curve. Then multiply each J ordinate by its proper multiplier.
Each of these products is next multiplied by the square of the
number of whole intervals it is distant from the end of the water-
plane. The sum of these moments multiplied by \ or f , the cube
of a whole interval (according to the Simpson's Rule applied) will
give the moment of inertia of the \ waterplane relatively to the first
ordinate. By multiplying by 2 the M of 1 for whole plane is obtained.
As we require, however, the moment of inertia of the waterplane,
relatively to the centre of the waterplane, a correction is necessary.
2nd, Find the Moment of Inertia of the Waterplaney relatively to
a Transverse Axis passing through the Centre of the Waterplane. —
Rule, Multiply the area of the waterplane by the square of its
distance from the first ordinate. This product subtracted from
the moment of inertia relatively to the first ordinate gives the
moment of inertia relatively to the axis passing through the
centre of gravity of the waterplane.
By applying this rule to the figure at the beginning of Example
20, we shall see that it agrees with S — .
CALCULATIONS.
293
No. of
Ord.
1
2
3
JOrds.
S. M.
* Products.
Squares of
Intervals.
Moments.
4-5
4-5
4-5
1
4
1
4-5
18
4-5
1
4
18
18
Common interval cubed _ 3^ _ g
36
9
Both halves
324
2
Moment relatively to 1st ordinate 648
Area of waterplane x (distance of centre of gravity from 1st
ordinate)^ = (9 x 6) x 3^ = 486
162 =
Moment of inertia relatively to trausveroe axis passine through centre of
WP.
As alreaxly stated, the moment of inertia divided by the dis-
placement in cubic feet gives the height of the longitudinal meta-
centre above the centre of buoyancy.
Calcvlationfor Longitudinal Metacentre above the Centre of Buoy-
ancy. — As an example, the half ordinates of a ship's waterplane are,
0, 4, 7, 9, 10, 8, 5, 2, 0. The common interval is 12 feet, the dis-
placement, 150 tons.
No. of
Ord.
iOrds.
S.M.
Prods.
Leverages.
Prods, of
Moments.
Levers.
Prods, for
M. of I.
1
1
2
4
4
16
1
16
1
16
3
7
2
14
2
28
2
66
4
9
4
36
3
108
8
824
5
10
2
20
4
80
4
320
6
8
4
32
5
160
5
800
7
5
2
10
6
60
6
860
8
2
4
8
7
56
7
392
9
1
8
8
i Longt. iuterval V =
136
508
12
(Com. int.)8 _
3 _
2268
576
544
Both halves 2
Area of waterplane 1088
C.G of W.P from
ord. 1.= 44*82
1306868
2 Both halves.
2612786 Moment of
inertia re-
latively to
ord. 1.
The result at the foot of the fourth column is area of water-
plane. Instead of multiplying the products obtained after using
294 KNOW YOUR OWN SHIP.
Simpson's Multipliers, by the square of the number of intervals in
one operation, it is done in two operations, as shown in the fifth
and seventh columns. This enables us to use the sixth column in
order to ascertain the position of the centre of gravity of the
waterplane, as shown in the calculation.
Area of waterplane x square of the distance of C.G of water-
plane from first ordinate = 1088 x (44*82)2 ^ 2185609.
2612736 Moment of inertia relatively to ordinate 1.
2185609
150 tons X 35 = 6250)427127 M. ofl. about axis passing through C.G of W.P.
81-35 feet = Height of longt. M.0 above O.B.
Example 25.
Alteration of THm. — The longitudinal metacentric height is
cliiefly used in order to ascertain the alteration to trim caused by
loaxling, discharging, or shifting weights or cargo on board a vessel.
The principle upon which Trim calculations are worked is fully
explained in Chapter VII., to which the reader should refer at this
stage. A variety of examples are dealt with at the end of that
chapter.
The moment altering the trim 1 inch, when a vessel is floating at
any particular draught, has been shown to be
D X G M p ? = displacement
:— — G M = metacentnc height.
W L X 12 W L = length of waterplane.
Suppose, in the previous example where the longitudinal meta-
centre was found to be 81*35 feet above the centre of buoyancy,
that a w^eight of 8 tons in the fore hold, and at a distance of 30
feet forward of the centre of gravity of the waterplane, is dis-
charged. What would be the alteration in trim ?
The moment altering the trim is 8 x 30 = 240 foot tons.
The "toDS per inch" is ^-^ = 2-59 tons.
^ 420
g
The decrease in drautrht is therefore = 3 "08 inches.
^ 2*59
The moment to change trim 1" =
150 X 82-35 G.M (supposing the C.G is found to be 1 foot below O.B) =
96 X 12
4117-5
38-4
= 10-72
Change in trim = ^^ = 22 '38 inches.
* 10-72
CALCULATIONS. 295
Suppose the vessel to have been floating upon even keel at a
draught of 6 feet before the weight was discharged. By discharg-
ing the 8-ton w^eight from forward, the vessel has changed trim
iri9-inches at the stem, and Il*19-inches at the stem.
Draught forward. Draught aft.
6' 0" 6' 0"
less 11-19 add 11-19
m
5'-0"-81 6' -11" -19
The mean draught has decreased 3 08 3*08
by 3-08"
Draught after weight discharged 4'-9"-73 6'-8"ai aft.
Example; 26.
Alter attun of Trim caused by Damage to Fore Peaky owing to
Collision. — As a further example of change of trim, suppose
this vessel has a fore-peak watertight bulkheaxl, at a distance of
15 feet from the stem, extending a considerable height above the
waterline (the length from stem to stem being 96 feet). Let the
draught be as before, 6 feet on even keel. Owing to collision,
this fore peak is damaged, and water is admitted from the sea.
A very important question in such a case is " What will be the
change in trim after the ship has again come to rest ] "
First of all, it is clear, that, owing to the loss of buoyancy in
the fore peak, the mean draught must have increased. Immedi-
ately the fore peak is perforated, and free communication estab-
lished with the water outside, the waterplane of the ship termin-
ates at the after side of the fore-peak bulkhead, the part before
the bulkhead providing neither buoyancy nor moment of inertia
of waterplane.
The loss of buoyancy in the fore peak must be compensated for
by the vessel increasing in draught, and obtaining the amount
lost from the reserve buoyancy abaft the peak bulkheaxl.
The amount of lost buoyancy must be found. This is, of
course, the voliunc of the fore peak below the 6-feet draught level.
Though there may be considerable space in the fore peak above
the 6-feet level, this never afforded buoyancy, being entirely
reserve buoyancy. Now that the peak is damaged, it is no longer
reserve buoyancy, so that the buoyancy to be dealt with is simply
that below the 6-feet level. This volume could easily be calcu-
lated by Simpson's Rules, as shown previously for displacement,
in fact, it is simply a calculation of the displacement of the fore
peak. Let the capacity be 210 cubic feet or 6 tons. The centre
of gravity of the waterplane between the stem post and the
296 KNOW YOUR OWN SHIP.
fore-peak bulkheaxl has next to be found, and also the centre of
buoyancy of the fore-peak displacement. Then axld together the
distance of the centre of gravity of the waterplane from the fore-
peak bulkhead, say, 38 feet, and the distance of the centre of
buoyancy of the fore peak from the bulkheaxl, say, 5 feet. The
simi 43 is the leverage used in ascertaining the moment altering
trim.
Moment to alter trim = 6 x 43 = 258 foot tons.
The length of the waterplane is now 96 - 15 = 81 feet.
The area of the waterplane will be less, let it be, say, 1030
square feet.
The shortening of the length of the waterplane and the reduc-
tion of its area will have reduced the longitudinal metacentric
height. Let it be now 74 feet.
The moment to alter trim 1 inch will be : —
150_x_74 J 3700 _ -, ..^
81 X 12 324
258
a xTun -
intact waterplane.
The ** tons per inch " - 12?2 = 2-46
^ 420
/»
The increase in mean drau(;ht = = 2*45 inches.
® 2 '45
The new draught will be : —
258
Total change in trim •—— = 22*6 inches = 11*3 inches, at each end of
® 11 -^2
Aft.
Forward.
6' 0''
6' 0"
2-46
2-45
6 2*45 6 2-45
-11-3 + 11-3
5 3-15 7 1-75
But the draught 7 feet If inches forward is at the collision
bulkhead, and we require the draught at the stem 15 feet
forward.
The length from G 6 of waterplane to stem is 38 + 15 = 53 feet
11-3" X 63 ,c T • V
^ = 16 •/ inches.
do
6' 2-46"
1 3-7
The draught at stem will be 7' - 6 -15"
CALCULATIOKS.
297
Example 27.
To find the area of a wedge-shaped figure, such as shown by
A B G in the adjoining figure,
which may be taken to re-
present one of the wedges of
immersion or emersion of a
rolling vessel, B C being a
plain curve. Let the whole
angle at A = 40 degrees.
Divide the angle at A into
a number of equal angular
intervals, so that the whole
number of radii may be suit-
able for the application of one 5
of Simpson's Rules.
Rule. — Measure the length of
each of the radii, and find their ^
half squares. Treat these half
squares as if they were ordi-
nates of a curve, by the applica-
tion of Simpson's Rules. If
the first of Simpson's Rules be
applied, then the sum of the half squares will require to be
multiplied by \ of the common angular interval, which must be
taken in circular measure.
Note, — Circular measure for 1 degree is '01745.
The calculation would be arranged as follows : —
No. of
Radius.
Radii
Squares of
Radii.
S. M.
Products.
1
2
3
4
5
20-0
20-5
21-0
21-5
22-0
400-0
420-2
441-0
462-2
484-0
1
4
2
4
1
400«0
1680-8
882-0
1848-8
484-0
Divide by 2 for half sqs. 2)5295-6
1745 2647-8
^^ = -0581
i of circular measure for 10** =
Area 153*8
296 KNOW YOUR OWN SHIP.
Example 28.
To Find the Vdluine of a Wedge of Immersion or Emersion, —
Suppose that the figure in the previous example haxl been one
of the sections in a wedge of immersion 100 feet long, then, by
dividing the length of the wedge into a suitable number of equal
intervals, and finding the area of the sections at each of these
intervals, and treating these areas as though they were ordinates
of a new curve by the application of one of Simpson's Exiles, the
volimie of the whole wedge would be ascertained.
Example 29.
To Find the Longitudinal Centre of Gravity of a Wedge, such as
that jv^t dealt with. — Rule. Multiply the area of each sectional
area by its distance from one extremity (call it x) of the wedge.
Treat the products as though they were ordinates of a new curve
of the same length as the wedge (100 feet), by the application of
one of Simpson's Rules ; the result so found will be the moment
of the wedge relatively to the extremity x. This moment, divided
by the voliune of the wedge, will give the longitudinal distance
of the centre of gravity from the extremity x.
Example 30.
To Find the Perpendicular Distance of the Centre of Gh^avity of
the For fi- Mentioned Wedge (see fig. in Example 27), relatively to the
Longitudinal Plane ZAS, which is perpendicular to tJie Radius A O.
— Rule. Divide the wedge into a number of longitudinal planes,
radiating from the edge A a at equi-angular intervals. Find the
moment of inertia of each of these longitudinal planes (5 in
number, see the fig.) relatively to A a, as explained in Example
20, page 290. Multiply each of these moments of inertia by the
cosines of the angles (see page 268) made by their respective
planes with the plane A C, and apply to these results the multi-
pliers for Simpson's First Rule. The sum of these products must
be multiplied by J of the common interval (using circular meas-
ure). The result is the moment of the wedge relatively to the
plane ZAS. This moment, divided by the volume of the wedge,
gives the distance of the centre of gravity of the wedge from the
longitudinal plane Z A S.-
When finding the centre of gravity of the wedge, as described
in this example, the volimie of the wedge is usually found as
follows (example 31) : —
CAtOUtAlJIONS.
ESAHFLB 31.
To Find Volume of Wedge of Immersion or Emernvm. — The wedge,
us hais been explained, is divided into 5 longitudinal planes radiat-
ing from A a, whicli planes have already been divided into a number
of equal intervals longitudinally, suitable for the application of
Simpson's Multipliere (this has been done in order to find the
moment of inertia in the previous example). Measure the
ordiuates, and compute their half squares. Treat these half
squares as though they were ordinates of a new curve by the
application of Simpson's Multipliers, and find the hypothetical
area in the usual way. The results thus obtained are moments
for eath of the longitudinal planes.
Use now these moments of planes as though they were ordinates
of another new curve by the application of Simpson's Multipliers.
The sum of products thus obtained, multiplied by J of the angular
interval, gives the volume of the wedge which ought to agree
with the result obtained by the method previously described in
Example 28, where the transverse sections were dealt with.
ESAUPLE 32.
Calculationfor Finding t}ie Position of Die Centre of Effort Itela-
tivelij to tJie Centre of Lateral Resistance. — In order to work out an
actual example, the Three-masted Schooner-rigged Vessel, page
213, is used. The sails are nnmbeied as shown upon the diagram.
The steps in the process of the calculation are fully explained in
Chapter VI. (Section VII.).
Diatancsfl of
Height of
Centres of Sails
Moments,
Centre of
Ko. of
Soil.
ai.Te't.
from Centre of
Sails above
CentcB of
Lateral
Vertical
Moments.
Before.
Feet.
Abaft
Feet.
Befoi'e.
Abiift.
Feet.
1
480
45
21,600
25
12,000
2
560
35
19,600
24
13,440
3
580
30
17,400
22
12,790
1
1000
1-2
12,000
28
28.000
aoo
15
4,500
50
16,000
6
1100
S
8,300
28
30,800
7
350
4
1,400
51
17,850
lEOO
30
45.000
26
39,000
9
810
26
8,500
60
17,000
Sum 76,100 08,700
300 KNOW YOUB OWN SHIP.
As the moments before the centre of lateral resistance prepon-
derate, it is evident that the centre of effort lies forward of the
centre of lateral resistance, and the distance is : —
75100 -63700^ 1.83 f,3t.
6210
The height of the centre of effort above the centre of lateral
resistance is : —
185860 ^29-92 feet.
6210
CALCULATIONS.
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304
KNOW TOUR OWN SHIP.
WETTED SURFACE AND SHELL DISPLACEMENT.
Up to 4' 0" Waterline.
o >
Half
CO.
Girths.
1
4-1
2
4-5
3
7-2
4
101
5
11-8
6
12-9
7
13-2
8
12-9
9
11-9
10
10-0
11
7-9
12
6-2
13
0-0
Pro-
ducts.
1
4
2
4
2
4
2
4
2
4
2
4
1
4-1
18-0
14-4
40-4
23-6
51-6
26-4
51-6
23-8
40-0
15-8
20-8
0-0
330-5
J longt. interval 4
1322
Both sides 2
Total Area of"
Immersed
Surface, which
is the Wetted
Surface,
2644
' sq. ft.
Up to 8' 0" WaterHne.
o •
1
2
3
4
5
6
7
8
9
10
11
12
13
Half
Girths.
8-0
9-4
12-3
14-7
16-1
17-0
17-3
17-0
16-1
14-3
12-2
9-4
4-0
1
4
2
4
2
4
2
4
2
4
2
4
1
Pro-
ducts.
8-0
37-6
24-6
58-8
32-2
68-0
34-6
68-0
32-2
57-2
24-4
37-6
4-0
487-2
4
1948-8
2^
Area 3897 6
Up to 12' 0" Waterline.
o .
1
2
3
4
5
6
7
8
9
10
11
12
13
Half
•
Girths.
1
12-5
15-1
4
16-7
2
18-8
4
20-1
2
21-0
4
21-3
2
21-0
4
20-1
2
18-4
4
16-2
2
13-6
4
8-0
1
Pro-
ducts.
12-5
60-4
88-4
76-2
40-2
84-0
42-6
84
40-2
78-6
32-4
54-0
8-0
640-5
^
2562
2
Area 5124
Let the average thickness of shell plating up to the load line be 8/20.
I
As the strakes of plating are alternately in and out the average thick
ness from the frames to the outside of the plating will be : —
2644
1
2644
20
3897
20
5124
20
8 + 4
20
— of an inch.
12
20
1
12
20
of a foot.
X ;rr =
1
20
35
2644
20
cubic feet displacement.
35 = 5-5
-r 35 = 7-3
3 '7 tons displacement at the 4 ft. waterline.
8 ft
})
))
))
})
jy
ff
12 ft.
tt
it
Notes on Wetted Surface Calculation.— The half girths of the frames,
measured from the top of the keel to the height of the particular waterlines, up
to which the areas are required, are taken at each section. These are Isreatea
as the ordinates of a new curve, and the area found, by the application of
one of Simpson's Rules, in the usual way. The area of the immersed keel,
stem, and stem frame, may be added to this.
Shell DisplacemerU Calculation.— The area of the immersed surface mnlti-
plied by the average thickness, from the frames to the outside of the plating,
gives the volume of displacement.
CALCULATIONS.
305
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CALCULATIONS.
307
DISPLACEMENT CALCULATION.
2nd Method of An^angement,
No. of
Top of
I'O"
2'0"
3' 0" 4' 0" 1
6'r
8'0"
lO'O"
12' 0"
Oi-d.
Keel.
W.L.
W.L.
W.L.
W.L.
W.L.
W.L.
W.L.
W.L.
\
2
•12
•66
108
1-42
1-89
3-00
4-60
6 •78
8-71
4
•12
4-46
6-60
7-92
8-80
10-14
10*86
11-26
11-40
r>
•12
7-80
9-90
10-87
m-44
11-90
11-98
11-96
11*90
8
•12
7-92
9 90
10-80
J. 11-25
11-71
11*86
11*90
11-86
10
-12
6-06
6 86
7-86
8-48
9-34
9-86
10-28
10-60
12
-00
136
2-23
2-80
317
3-80
4-24
4^66
4*98
a
•60
28-22
36-6fi
41-67
45-03
49-89
63-37
66*77
69-34
2a
1-20
66-44
7312
83-34
90 06
99-78
106-74
118*64
118 68
(01
•06
•06
-06
•06
-06
•06
-07
-30
1-00
3
•12
216
3-66
4-76
6-70
7 40
8-80
9-88
10-65
5
•12
6-70
8-65
9-80
10-61
11-36
11-66
11-76
11-76
7
•12
8-40
10-22
11-06
11-61
11-90
12*00
12*00
11*98
9 -12
7-00
8-70
9-74
10-38
11-02
11-81
11*46
11*61
11 -12
3-36
4-72
6 64
6-06
6-93
7*60
910
8*46
Sums of
(^13 -00
0-00
000
0-00
0-00
•10
•16
-18
•22
Func-
tions
=of Hori-
1-86
84-11
109-12
124-29
134-27
148-66
168-82
168-21
174*26
Simpson's ) ,
^Multl- )■ *
pliers )
1
i
1
zontal i
2
\
2
i
Areas.
•46 84-11
27-28
124-29 33-66
29710 7916 836*42 87-12
•
84-11
124*29
297-10 386-42
•46
27-28
67-13 79-16
Sum of Multiples \
of Functions /
111-86
•
296-98
■
740^87
111-85
296-98
74087
1248^07
Multiplier for Displacem
ent •60i
J
•608
(
•608
t
-608
1
89480
237684
692296
994466
671100
1781880
4442220 7468420
Tons C
;8 -00480
180-66884
460*14496 766*78666
Shell displacement to add. See page 804.
CALCULATION FOR "TONS PER INCH IMMERSION."
2* 0"
W.L,
4'0"
W.L.
8'0"
W.L.
12' 0"
W.L.
rSum of Functions
= X of Horizontal
i. ^ Areas.
Areas of Waterlines
« « ,« 109-12
2x2x12 _ jg
184-27
16
168-82
16
174*25
16
4-20)1746-92
420)2148-82
420)268812
420)2788
Tons per Inch 4-16
6-11
6*03
6-63
Notes on Displacement CaleultUicn, 2nd Method. — This calculation involves somewliat less
labour than the first method. It is simply a method of using Simpson's ^ Multipliers through-
out All the even ordinates are put in the top column, and the sum of them, a, to multiplied by
2, and placed in the 2a line. In the column below, the odd ordinates are placed together with
half of the endmost ordinates, and these are added together, including the 2a line. By tills pro-
cess we have simply used, 4, 2, 1, 2 and so on, as Simpson's Multipliers, instead of 1, 4, 2, 4, etc.
The sum of these horizontal functions are treated by Simpson's | Multipliers, and ttie displace-
ments found as before. It will be noted that the multiplier for displacement is *608, this being
•162 x '2 (for horizontal ^ Simpson's Multipliers) x 2 (for vertical i Simpson's MultipUers) s *608.
Tons per Inch.— The area of each parttcnlar wateirplane ia obtained by multiplying the sum
of the functions of the horizontal half areas by 2 for ^ Simpson's Multipliers, by 3 for the
other side, and by | of the longitudinal intervals
2x2x12 ^^^
308
KNOW TOUR OWN SHIP.
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I
OALOITLATIOKB.
CALCULATION FOR LONGITUDINAL CENTRES
OF BUOYANCY.
2nd Method of Arrangertient.
II
|i
W.L.
2'0'
W.L.
K
fl-O"
wT.
K
W.L.
= 1011'.
10
2
o'Stt
i
HB
.i|
B11»
41flO
4-BO
46-64
8s-ao
81-91
■
8-00
177-74
Mfi-sa
846-87
STau
S00-7S
BIS-OT
3M-8S
884-64
is.
IS
10
■48
J
3Sfi'4S
0-00
mm
00
O-M
o-oc
O'OO
i
8816
630 -H
W-48
16 -00
180
0-00
M-00
869 '28
0-00
84-60
1
SISSH
67 -7*
7Bl-fl«
.,.,.
891-80
835-06
977-M
*
2-40 636'S8 ISf-eS
LodgittuUnBL Inlervol, = 12
7S1'BS aoi-M
761-68
«9e-si
3M-98H«30-7*
408-43
1830-74
7M87)4*90-Si
B-OS
n.
lSM-44 4M'g8
1243-07)7406-68
(t.
PIKT5.
Longitudinal Oentrt qf Svo^ont^.— Id this cdcnUtion, the ordinates (aee
Dieplscement Sheet) for the varions waterplanes are maltiplied by their
respective leverageB (intervala) from the flret ordinate, and the moments so
obtained are treated b; Simpson's HultiplieTS. In the abore calcahitlDi],
the centre of buoyancy is worked for four separate dranghta, giving four
separate results.
The sums of moments are next treated by Simpson's Haltipliers, and the
new sum is divided by the "sum of multiples of fnnctioDs" (from the
Displacement Sheet). This result^ multiplied by the common interval, gives
the position of the longitudinal centre of bnoyancy ratatiTely to the first
310
KNOW TOUR OWN SHIP.
CALCULATION FOR HEIGHTS OF TRANSVERSE META-
CENTRES ABOVE CENTRES OF BUOYANCY.
2nd Method of Arrangement,
No. of
Ord.
2
4
6
8
10
12
a
2a
5
7
9
11
(J) 13
2^ 0" W.L.
Cubes of
^ Ordinates.
4' 0" W.L.
Cubes of
i^ Ordinates.
8' 0" W.L.
Cubes of
^ Ordinates.
12' r W.L.
Cubes of
i Ordinates.
1-25
287*49
970-29
970-29
321*41
11*08
2561-81
5123*62
0*00
48-62
647*21
1067*46
658*50
105*15
0*00
Functions of Cubes, 7650*56
5-33
2295168
2295168
3825280
2380*)40777*4848
M.C. above C,B.=17*13ft.
6*75
681*47
1497*19
1423*82
609*80
31*85
4250*88
8501*76
0*00
185-19
1160*93
1524*84
1118*38
221*44
0*00
12712*64
5-33
8813762
3813762
6356270
?)67757-8382
o>
CO
97*33
1277*28
1719-37
1664*00
955*67
76*22
5789-87
11579*74
0*00
681*47
1581*16
1728 00
1446*78
438*97
0-01
17466*08
5*38
*
6236824
6236824
8728040
10*72ft. 2
)93040*9064
5 6*90ft.
660-77
1481*54
1685-15
1664*00
1157-62
123-60
6772-58
13546-16
4-00
1207*94
1622*23
1719*87
1524-84
605-49
•04
20229*07
6*33
6068721
6068721
10114636
94
)107820*9431
4*07ft
Mull^lier for
Moment of
Inertia.
Moment
Inertia.
of
* rs displacement in cubic feet
With the previous explanations the only point in this calculation
needing comment is the multiplier 5*33.
12x2x2
3x3
= 5-33.
Where 12 is the longitudinal interval
2 is for half Simpson's Multipliers.
2 is for both halves of waterplane.
3 is for J of cubes.
3 is for I of longitudinal interval.
OALCDTiATIOtra.
a -es
1 Is
5 fl i
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ri
m
;:s^|?3s:s?$3^^
^i 3
■ -I
I 9
21" 1
312
KNOW TOUR OWN SHIP.
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CALCULATIONS.
313
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314
KNOW TOUR OWN SHIP.
By means of the results given in the foregoing calculations,
curves may be constructed, see figs. 138 and 139 as described
and illustrated in the earlier chapters of this book, by which
means any of the quantities or distances may be ascertained for
any intermediate draught or waterline.
Care should be taken in noting that, while the draughts are
measured from the bottom of the keel, the calculations have been
for waterlines measured from the top of the keel, and need to be
set off accordingly in constructing the curves. When a vessel
trims by the head or the stem, the mean draught is that worked
to, in taking any particulars from the curves
Fig. 138.— Curves of Displacement— Tons per Inch Immkesion —
Longitudinal Centres of Buoyancy set off from the Aft
Side of the After Stern Post.
Note. — 100 on the horizontal scale of tons equals 1 ton for the tons per
inch immersion, and 10 feet for the longitudinal centres of buoyancy.
Stability Calculations. — Fig. 140 shows our vessel keeled
CALCULATIONS.
315
to an angle of 14**, at which angle the stability is computed in the
stability calculation, page 320.
In fig. 140, V = the volume of the wedge of immersion, or,
the wedge of emersion.
BR is what the righting arm of stability would be if the centre of grayity
coincided with the centre of buoyancy in the upright condition. It is per-
pendicular to the vertical line through B'.
BR may therefore be called the lever of stability produced by design or
form. It is usually called the lever of statical surface stability.
Fig. 139.— Curves op Vbbtical Centres of Buoyancy— Transverse
Metacentrks — Longitudinal Metacentres (note, 3 feet on the
Vertical Scale Reprbsbntb 100 feet).
G is the centre of gravity of the ship, its position being governed by the
loading and position of weights carried.
The lever of statical stability is therefore : —
BR - BC - GZ BC - BG X .sme of angle of ir.
316
KNOW TOUR OWN SHIP.
The moment of statical surface stability is BR x displacement in tons.
The moment of statical stability is GZ x D (displacement in tons).
gh and ^h' are perpendicular to W'L'.
B' is the position of the centre of buoyancy at 14° of inclination.
g^ g' are the centres of gravity of the wedges of immersion and emersion.
BB
,_Vxgr/
D
BR =
Yxhh'
D
G Z = -1-^ - BG. xsine of 14°
— jT— - (BG. sine of 14°) |
Fig. 140.
Fig. 141 shows the sections of our vessel prepared for the
stability calculation. The calculation is divided into two parts,
the first being of a preliminary nature in order to obtain results
which are transferred to the combination table in the second part.
From the stability sections, the ordinates are measured for
the upright, and the two inclined, waterplanes, for both the
immersed and emerged wedges, and inserted in their proper
columns in the preliminary tables.
CALCULATIONS. 317
The three results obtained in the preliminary tables almost
explain themselves, after the examples worked in Section I. of
this chapter.
(1) By treating the ordinates by Simpson's Multipliers, the total area of the
new horizontal waterplane is obtained, W L' (fig. 140), — the immersed and
emerged sides being added together. This is only necessary for the third
waterplane in the calculation. See Example 10. Section 1 of this chapter.
(2) By treating the half squares of ordinates by Simpson's Multipliers, it
is found on which side of the inclined waterplane there is a preponderance
of moment. In this case, the immersed is the greater. The centre of
gravit}*^ of the waterplane, therefore, lies towards this side. By subtracting
the emerged side from the immersed, and dividing by 2 for ^ squares, and
multiplying by ^ of the longitudinal interval, the preponderating moment is
ascertained. This, divided by the area of the same inclined waterplane,
gives the distance the centre of gravity is out from the longitudinal middle
line of the waterplane on the immersed side. See Example 17.
It will now be seen that the area was necessary in order to find the transverse
centre of gravity of the whole inclined waterplane.
(3) By cubing the } ordinates of the three planes, and ultimately taking
one-third of them, we obtain the moment of inertia which is necessary in
order to find the moments of the wedges. See example 30.
In fig. 141 the wedges of immersion and emersion have been
drawn as though the waterplanes for all angles of inclination
intersected at the original fore and aft centre line of the upright
waterplane. In reality, these waterplanes do not, at least for
considerable inclinations, for it is well known to the reader that the
volume of the wedge of immersion so obtained, would in all
probability, differ from the volume of the wedge of emersion. So
a correction becomes necessary in order to arrive at an accurate
result. If the volume of the wedge of immersion be larger than
that of the wedge of emersion, it is clear that the vessel is drawing
more water in the diagram than she does in reality. By dividing
the difference in volume of the two wedges as calculated, by the
area of the waterplane, the thickness of the correcting layer to be
deducted from the draught is ascertained. Had the immersed
wedge been less than the emerged, the difference in voliune of the
two wedges divided by the area of the waterplane, would give the
thickness of the layer to be added to the draught. In the com-
bination table, the volume of the immersed and emerged wedges
are calculated as explained in Example 31, and the thickness of
the correcting layer is obtained.
In our vessel we see that the volume of the wedge of immersion
exceeds that of the wedge of emersion by 89*75 cubic feet, and the
thickness of the correcting layer is '03 feet. And as the centre
of gravity of the inclined waterplane which represents the centre
of gravity of the correcting layer is '25 feet (see preliminary table)
towards the immersed side, the moment of the wedges is in excess.
318 KNOW TOUR OWN SHIP.
and the moment of the layer must be deducted from the moment of
the wedges. Had the centre of gravity of this layer lain towards
the opposite side, its moment would have had to be added.
The last operation in the combination table is to find the
moment of the wedges. This process has been fully explained in
Example 30. The sums of the fimctions of the cubes of the
ordinates for the waterplanes of both wedges, are transferred from
the preliminary tables. These functions are treated by Simpson's
Multipliers, and also by the cosines of the angles of inclination,
obtaining " functions of cubes for moments of wedges." The sum
of these functions for moments is divided by 3, as J of cubes of
ordinates is required for moment of inertia of waterplanes. The
result is multiplied by ^ of the angular interval, and this by J of
the longitudinal interval giving moment of the wedges relatively
to a plane passing through xl^y perpendicular to W, N, L' (see
fig. 140). From the moment of wedges is subtracted the correct-
ing moment for the layer, and the remainder divided by the
displacement gives the distance BR (fig. 140) produced by the
transference of the wedge WNW to L'NL, a distance hh\
To obtain the righting lever GZ, subtract BC from BR
(BC = BG multiplied by the sine of the angle BGC, which
is 14°).
G Z X displacement = Righting moment in foot tons.
As a check upon the G Z, when calculated for small angles of
inclination (before the deck edge is immersed), not exceeding 10°
or 15^
G M X Sine of angle = GZ.
2 feet X '2419 =- 'dSSS which is approximately correct.
Note, — The metacentre was found to be 4*07 feet above the centre of
buoyancy and the metacentric height was assumed to be 2 feet.
In order to construct a curve of stability a succession of calcu-
lations, identical to that we have just described, would have to be
made for the vessel inclined to a succession of angles of inclination
in order to find the G Z's at each inclination.
CALCDLATIONB.
FjG, 141. — SSCTIONH FOK CALCULATION OF STATICAL STABILITY.
320
KNOW YOUR OWN SHIP.
CALCULATION FOR THE STABILITY OF A VEg
See fig.
PSELIMIl
Up
Immersed Wedge.
No. of
Ordinates.
Multi-
Functions of
Squares of
Multi-
Functions of
Cubes of
Multi-
• Functions '
Section.
pliers.
Ordinates.
Ordinates.
pliers.
Squares.
Ordinates.
pliers.
Cubes.
1
2-00
4 00
1
4-00
8-00
1
8-00
2
8-71
75-86
4
303-44
660-77
4
2643-08
3
10-65
113-42
2
226-84
1207-94
2
2415-88
4
11-40
129-96
4
519-84
1481-54
4
5926-16
5
11-75
138-06
2
276-12
1622-23
2
3244-46
6
11-90
141-61
4
566-44
1685-15
4
6740*60
7
11-98
143-52
2
287-04
1719-87
2
8438*74
8
11-85
140-42
4
561-68
1664-00
4
6656-00
9
11-51
132-48
2
264*96
1524-84
2
3049-68
10
10-50
110-25
4
441-00
1157-62
4
4630*48
11
8-46
71-57
3
143-14
605-49
2
1210-98
12
4-98
24-80
4
99-20
128-50
4
494-00
13
44
•19
1
-19
•08
J
-08
3693-89
40458*14
3
80916-28 For
1
wet
Prblimii
Waterplane inc
Immersed Wedge.
1
2-4
6-7
1
5-7
13-8-
1
13*8
2
9-5
90-2
4
360-8
857-8
4
8429-2
3
11 -0
121-0
3
2420
1331-0
2
2662-0
4
11-6
134-5
4
538-0
1560-8
4
6243*3
5
11-8
189-2
2
278-4
16430
2
3286-0
6
120
144-0
4
576-0
1728-0
4
6913-0
7
120
144-0
2
288-0
17280
2
3456
8
11-9
141-6
4
566-4
1685-1
4
6740-4
9
11-6
184-5
2
269-0
1560-8
3
3131-6
10
10-7
114-4
4
457-6
1225-0
4
49000
11
8-7
75-6
2
151-2
658-5
3
1817
12
5-2
27-0
4
108-0
140-6
4
563-4
13
•4
•1
1
-1
•0
1
•0
3841-2
42648*6 ImiiK
wed
40197-0 Emm
iro^
83840-6 Stun
botl
wed
CALCULATIONS.
321
INCLINED TO AN ANGLE OF 14 DEGREES,
for Drawings.
Table I.
Waterplane.
Emerged Wedge.
No. of
Section.
Ordinates.
Miilti- Functions of
pliers. Ordinates.
Squares of
Ordinates.
Multi-
pliers.
Functions of
Squares.
Cubes of
Ordinates.
Multi-
pliers.
Sams as Imukbskd Wrdge.
Functions of
Cubes.
Table II.
to an angle of 7°.
Emerged Wedge.
1
1-8
3-2
1 3-2
6-8
1
5-8
7-9 ,
62-4
4 249-6
4930
4
1972-0
10-8
106-0
2 2120
1092-7
2
2185-4
11-4 1
129-9
4 519-6
1481-5
4
5926-0
11-9
141-6
2 283-2
1685 1
2
3370-2
12 1
146-4
4 585-6
1771-5
4
7086-0
121
146-4
2 292-8
1771-5
2
35430
120
1440
4 576-0
1728-0
4
6912-0
11-5
132-2
2 264-4
1520-8
2
3041-6
10-4
108-1
4 432-4
1124-8
4
4499 2
8-4 1
70-5
2 1410
592-7.
2
1185-4
4-9
24-0
4 96
117-6
4
470-4
•4
•1
1 1
•0
1
•0
3655-9
40197-0
1
2
3
4
5
a
7
8
9
10
11
12
13
322
KNOW YOUR OWN SHIP.
CALCULATION FOR THE STABILITY OF A VESI
PllELIMIN
(Waterplane incli
Immersed Wedge.
No. of
Section.
1
2
3
4
5
6
7
8
9
10
11
12
13
Ordinates.
Multi-
pliers.
31
1
10-3
4
11-4
2
11-8
4
12-0
2
120
4
12-2
2
12-2
4
lit)
2
111
4
9-2
2
6'4
4
•4
1
Functions of
Ordinates.
31
41-2
22-8
47-2
24-0
48-0
24-4
48-8
23-8
44-4
18-4
21-6
•4
Squares of
Ordinates.
Multi- Functions of
pliers. Squares.
9-6
1060
129-9
139-2
144-0
144-0
148-8
148-8
141-6
123-2
84-6
291
•1
1
4
2
4
2
4
2
4
2
4
2
4
1
9-6
424
259-8
556 8
288-0
676-0
297-6
696-2
283-2
492-8
169-2
116-4
•1
Cubes of
Multi-
Ordinates.
pliers.
29-7
1
1092-7
4
1481-6
2
1643-0
4
1728-0
2
17280
4
1816-8
2
1815-8
4
1686-1
2
1367-6
4
778-6
2
167-4
4
•0
1
Functions o:
Cubes.
29-7
4370-8
2963-0
6672-0
3466-0
6912-0
3631-6
7263-2
3370-2
6470-4
1567-2
629-6
Sum of functions / Immersed, 368 - 1
of Ordinates, \ Emerged, 346-4
Total, 714-5
^ of longitudinal interval, . 4
Total area of Waterplane, 2858-0
Immersed side, . 4068-7
Emerged side, . 3707-2
Fori squares, . 2)361-6 difference
46226 '7 Immeri
wedg
41419-2 Emergt
wedg
^ longitudinal interval,
87644-9 Sum f o
180-75 preponderance of i^ both
squares on im-— i— i— wedgt
mersed side.
^^plane ^**®^' } 2858)723-00 moment.
Centre of gravity =
-25 of a foot towards immersed side.
CALCULATIONS.
323
uINED TO AN ANGLE OF 14 DEGREES— con^inw^i.
.E III.
I angle of 14**.)
Emerged "Wedge.
of
Ordinates.
Multi-
1
Functions of ,
Squares of iMulti-
Functions of
Cubes of
Multi-
Functions of
rion.
pliers.
Ordinates.
Oi-dinates. j pliers.
Squares.
Ordinates.
pliers.
Cubes.
1
1-6
1
1-6
2-5
1
2-5
40
1
40
2
7-3
4
29-2
63-2
4
212-8
389-0
4
1666-0
3
100
2
20
1000
2
200
1000-0
2
2000-0
4
11-5
4
46
132-2
4
528-8
1620-8
4
6083-2
5
12 1
2
24-2
146-4
2
292-8
1771-5
2
3643-0
6
12 4
4
49-6
153-7
4
614-8
1906-6
4
7626-4
7
12-4
2
24-8
153-7
2
307-4
1906-6
2
8813-2
8
12-2
4
48-8
148-8
4
695-2
1815-8
4
7263-2
9
11-8
2
23-6
139-2
2
278-4
1643
2
8286-0
10
10-5
4
42-0
110-2
4
440-8
1167-6
4
4880-4
11
8-3
2
16-6
68-8
2
137-6
671-7
2
1143-4
12
4-9
4
19-6
24-0
4
96-0
117-6
4
470-4
13
•4
1
•4
•1
1
-1
•0
1
•0
346-4
3707 2
41419-2
324
KNOW YOUR OWN SHIP.
COMBINATION TABLE FOR STABILITY AT 14° INCLINATION.
Immebsed Wedge.
Emerged Wedge.
Angles of
Inclina-
tion.
Functions of
Squares of
Ordinates.
Multi-
pliers.
Functions of Squares
of Ordinates for
Volume of Wedge.
Functions of
Squares of
Ordinates.
Multi-
pliers.
Functions of Squares
of Oi-dlnates for
Volume of Wedge.
0'
7"
14-
8693-8
8841-2
4068-7
1
4
1
3693-8
15364-8
4068-7
3693-8
3655-9
3707-2
1
4
1
3693-8
14628-6
3707-2
Immersed wedge,
Emerged „
For half squares,
i of angular Interval,
23127-3
22024-6
22024-6
2) 1102-7 difference.
551-35 preponderance of half squares in immersed
wedge.
•0407
i of longitudln{^l interval,
Excess In volume of immersed
wedge,
385945
2205400
22-439945
4
89-769780
Correcting Layer.
89-769 X -26 (centre of gravity of waterplane
towards immersed side. See
Preliminai-y Table III.).
=22*439 Moment for Layer.
Area of waterplane,
2858)89-759
'03 of a foot Thickness of Layer.
Both Wedges,
Angles of
Inc ina-
tion.
Sums of Functions
of Cubes of
Ordinates.
Multi-
pliers.
Products of Func-
tions of Cubes.
Cosines of
Angles of In-
clination.
Functions of Cubes
for Moments of
Wedges.
0°
7-
14"
80916-28
82840-60
87644-90
1
4
1
80916-28
331362-40
87644-90
•9702
•9926
1-0000
78604*9
328877*1
87644*9
i of cubes
I of angular inclination,
I of longitudinal interval,
Moment of wedges, .
(Subtract) Correction for layer,
Disp. in cubic feet, .
3)496026*9
166008*9
*0407
6716*8
4
26863*2
-22*4
26462*8)26840*8
BR=s
BGxSine of Angle = 2*07 x *2419ss
Righting Arm GZs
1*01
•60
*606
Righting Moment of Stability =GZx Displacement in Tons ='506x766*78^881 -66 foot tons.
Righting Moment wlien inclined to an angle of 14* =381*66 foot tons.
325
APPENDIX A. •
The Author desires, in conclusion, to call the attention of such of his
readers as have some mathematical attainments to an able Paper, read
before the Institute of Marine Engineers, on Jan. 12, 1892, by John A.
Rowe, Esq., Surveyor to the Board of Trade.* From this Paper, which was
kindly placed at his disposal, he has made the following extract, which
will be found of much interest : —
DYNAMIC STABILITY AND OSCILLATIONS AMONG WAVES.
"Most of you are aware that in computing the rolling period of a ship —
that is, the time in seconds she will take to roll from the vertical and back
again — she is somehow or other regarded as a pendulum. This is a correct
view to take of the matter if the siibject is approached in a proper direction.
But many able men have been perplexed by what has appeared to be the
contradiction between theory and practice. For instance, most of you are
aware that the period T of a bob-pendulum in seconds is :
T = 3-1416 X ^ /Length^in feet ^ g.^^^g ^ Jh ^ .554 ^ ^"j;
V Gravity V 32
L is the length of the pendulum in feet.
In this formula it is clear that the x)eriod of a pendulum varies as the
square root of its length.
For the smooth water period of a ship the formula is somewhat different,
and is as follows : —
T = 3-1416 / Radius of Gyration squ ared _ .gg^ ^ f B?_
\/ Gravity x Metacentric Height \/ G M
The radius of gyration and the metacentric height to be in feet.
An examination of this formula reveals the fact that a vessel's rolling
period varies directly as the radius of gyration, and inversely as the square
root of the metacentric height. If G M be increased in length, the vessel's
period will be shortened, and she will become a quicker roller than before.
Bat practical men looking at the usual diagrams, have reasoned thus:^
* The length G M is the distance between tne vessel's point of oscillation
and her centre of gravity. If there is any pendulum-like motion in the
ship it is of necessity about G or M, at a length G M.'
But the formula T = '554 x /-£i_ shows clearly enough that whatever
be the equivalent pendulum length it is not G M but is something entirely
different. The following fig. has been constructed by the writer in the hope
of simplifying some points not generally understood.
The vessel is shown upright on the wave-slope. In this position the
force of buoyancy, which acts at right angles to the wave surface^ as it acts
at right angles to the surface of smooth water, creates a righting arm G Z.
This length in feet, multiplied by the ship's weight in tons, is what we
have called the vessel's righting moment in foot-tons. In the position we
* Now Chief Examiner of Bngineen to the Board of Trade.
APPBNDIX.
h&ve shown her, it iB obrious that this poner, usaallj regarded bb the
power of recovery, Btarta the veaael rolling ; aod if, after ahe had acquired
gurface to the sea she would roll through the angle G M on each Bide of
APPENDIX, 327
the vertical, and gradually extinguish the range of oscillation by the fluid
resistance offered to the immersed portion of the hull.
Again, if GO and MT be drawn at right angles to GM, and TO drawn
parallel to G M, we obtain a parallelogram of forces, whose resultant M
may be regarded as the buoyant force which equals the weight of the ship,
and whose components are GM and MT. As GM is acting upward
tlirough the vessel's centre line we may disregard it, and direct our atten-
tion exclusively to the component M T, whose direction is shown by arrow,
and whose amount is M x sine of the angle of inclination.
Let the effective angle of the wave-slope be 9**, the vessel's weight
10,000 tons, her metacentric height 6 feet. Find the turning moment about
G, the vessel's centre of gravity.
The component M T = M x sine of 9° = 10,000 tons x -156 = 1560 tons.
This force of 1560 acts at the end of the lever G M = 6 feet ; therefore,
the righting, or in this case, the turning moment
= 1560 tons X 6 feet = 9360 foot-tons.
But the righting moment is the weight of the ship multiplied by the
righting arm. What is the product of these quantities ?
Ft. Foot.
G Z, the righting arm = G M x sine of 9° = 6 x -156 = '936.
Tons'. Foot.
Righting moment 10,000 x '936 = 9360 foot-tons.
Both calculations declare the righting moment to be 9360 foot-tons.
In other words, the weight of the ship into the righting arm G Z = the
component MT into the metacentric height. If now we plot Y as the
centre of gyration, we shall be able to realise the nature of the force
tending to produce motion, and the character of the resistance offered to it.
Let us for a moment suppose that G is a fixed point — the ship's fulcrum.
Let us also regard the ship as a portion of a huge wheel (a p-^rtion of a fly-
wheel) its radius of gyration being G Y.
By an examination of the fig. it will be seen that the greater GM is
(with a given horizontal force M T) the greater is the turning moment.
And the smaller the radius of gyration G Y, the smaller will be the resist-
ance and the quicker will be the motion of oscillation.
To obtain great stability and quick motion, we must increase the leverage
G M, and reduce the pendulum length G Y ; to obtain moderate stability,
but a slow angular motion, and, tlierefore, a comfortable vessel at sea, and
one offering a steady gun-platform, we must diminish the leverage G M and
increase the length of G Y.
With regard to GY, which is obtained by dividing the vessel's moment
of inertia about G by the sum of the weights, and extracting the square
root, it is evident that it can be of great length only in a large vessel. In
a small vessel, GY can be increased by placing movable weights towards
the bulwarks, but no such change as this will be sufficient to make the
radius of gyration great enough to give rise to a slow rate of oscillation.
An easy motion in small crafts may be obtained by shortening GM, but
this may give rise to want of stability. Hence the difficulty of builders to
ntake a perfect ship. They have to steer between Scyila and Charybdis.
Worse still, they strive to please shipowners, who know but little of the
difficulties of naval architecture ; and to please themselves, with the result
that they sometimes please neither. . . .
Wave action upon ships, stores wave energy in ships to an extent depending
on their weight and length of righting arm ; and the manner of ascertaining
328 APPENDIX.
the amount of work put into the before-mentioned ship is as follows : — The
force MT = 1560 tons, becomes nil when the vessel's deck is parallel to
the wave-slope or to a smooth sea. Therefore the mean force acting to turn
the ship at M about the centre G is — - = — -_ = 780 tons. This mewn
^ 2 2
force acts through the space M T = M G x tangent of the angle of inclina-
tion = 6 feet X -158 = '948 foot. And 780 tons x -948 foot = 739*44 foot
tons dynamic stability. . . .
Storm-waves produce violent rolling in the largest of floating stiuctures,
and these structures are occasionally brought to rest by a sudden and com-
plete expenditure of their stored energy. And the greater the energy in
the vessel — i.e., the heavier the ship, and the quicker the motion, the more
tremendous is the blow she can inflict upon an approaching wave. But,
unhappily, when the momentum of an ocean wave is not only resisted by
a vessel's hull, but is increased by the dynamic energy of the ship, a climax
occurs, the severity of the blow is manifested by the vessel ceasing to roll
(her energy being expended), and by the wave bursting high above the
decks and sweeping them from end to end. This condition of things, as
about to happen, the writer wishes to convey in the rough sketch, by
arrows, showing the direction of the ship's oscillation and the wave's
advance. The fig. is not by any moans to scale." The projections E K on
each side of the diagram are short lengths of troughs which, in Mr. Rowe's
opinion, would prevent rolling. They are open ended, and the dimensions
would vary with the weight of the ship and the metacentric height.
They would probably render torpedo boats habitable in choppy seas and
stormy weather.* — (Krom paper on "Stability and Motions of a Vessel
among Waves,'* by John A. Rowe. Part ii., p. 10, et seq,)
APPENDIX B.
TEST QUESTIONS.!
CHAPTER I.
1. What is displacement? What is a displacement curvet Explain its
construction and use.
2. What is deadweight? What is a deadweight scale, and how is it
constructed ? ^
3. What is meant by " tons per inch " immersion ? Give and explain the
rule for " tons per inch" immersion.
4. Explain how a curve of "tons per inch" immersion is constructed,
and show clearly its use.
5. What is a coefficient of displacement ? State approximately the co-
efficient for an average cargo steamer, and a fine passenger steamer.
6. What is the weight of 1 cubic foot of salt water and 1 cubic foot of
fresh water ? How many cubic feet of salt water, and also of fresh water, are
there in 1 ton ?
7. Find the displacement of a box ship floating light in sea water at a
* By instantly exhausting the energy derived from each wave. These troughs would
prevent the accumulation of energy and therefore limit the effect of wave action to that
due to the passing of one wave only under the ship's bottom.
t Many of these questions are taken from Science and Art Examination Papers.
APPENDIX. 329
draught of 5 feet forward and 6 feet aft. The length is 100 feet ; the
breadth 20 feet (use mean draught). Ans, 314 '2 tons.
8. When loaded, the box ship in the previous question draws 12 feet of
water fore and aft. What is the dead weignt ? ^ris. 371*5 tons.
9. A ship of 1000 tons displacement, loaded, is floating in sea water.
What will be the change in draught in passing into river water! The
** tons per inch " at the load line is 9. Aiis. Draught increases 1 '7 inches.
10. A steamer on a voyage burns 200 tons of coal. The " tons per inch "
is 24. What is the approximate change in draught! Ans, Draught de-
creases 8*3 inches.
11. A vessel is 200 feet long, 30 feet broad, and of 16 feet depth to top of
weather deck at amidships. The freeboard is, say, 2 feet, and the coefficient
of fineness '65. What is her displacement in salt water? Atis, 1560 tons.
CHAPTER II.
12. What is meant by saying that a vessel has a righting or a capsizing
moment ?
13. Define the term " centre of gravity."
14. A ship has a displacement of 2000 tons when floating at a certain
draught ; 100 tons are then placed on deck at a height of 9 feet above the
centre of gravity of the ship as it was before the weight was placed on
board. Find the alteration in the position of the centre of gravity. Ans,
Centre of gravity is raised '42 foot.
15. A ship, with a displacement of 2000 tons, has a weight of 100 tons,
already on board on the centre of the upper deck, moved 8 feet to the port
side. Find the distance the centre of gravity has shifted. Ans. '4 foot.
16. The centre of gravity of a ship is 12 feet from the bottom of the keel.
In this condition her displacement is 2500 tons. She is then loaded in the
following manner : — 100 tons are placed 9 feet above the bottom of the keel,
300 tons 14 feet, and 500 tons 12 feet. Find the new position of the centre
of gravity from the bottom of the keel. Ans, 12*08 feet.
CHAPTER III.
17. What is meant by buoyancy, reserve buoyancy, centre of buoyancy ?
18. How do water pressures act ? Which of them aff'ord support %
19. What is meant by sheer ? and explain its use.
20. Of what value are deck erections as regards buoyancy 1
21. What is the vertical centre of buoyancy 1 also longitudinal centre of
buoyancy %
22. Show how curves of longitudinal and vertical centres of buoyancy
are constructed.
23. Supposing a ship's longitudinal centres of buoyancy to be in the
middle of the length at every draught when floating on even keel, and she
is loaded in the following manner : —
10 tons are placed 30 feet forward of the centre of buoyancy
120 .. 50
500
400
15
150
II II II
60 ,, ,, ,,
70 feet aft ,, ,,
60 ,, ,, .,
25 ,, ,, ,,
330 APPENDIX.
Where would a weight of 200 tons need to be placed on board to bring her
again on even keel ? Ans, 18*25 feet aft of the centre of buoyancy.
24. Why does a ship increase in draught on a comparatively small com-
partment being damaged below the water level, into which the sea enters ?
25. What is meant by camber, and why is it given to a vessel ? State
the rule for the minimum.
26. A box ship is 100 feet long, 20 feet broad, and floats at 6 feet draught.
Calculate the amount of upward water pressure in lbs. Ants, 768,000 lbs.
CHAPTER IV.
27. Enumerate in order of importance the principal strains to which a
ship may be subject.
28. State clearly what strains a ship may experience when floating light
and in calm water.
29. Show how strains may be decreased or enormously increased in the
operation of loading.
30. Describe the strains experienced by a ship among waves — fore and aft
and athwartships.
81. Explain the term " unequal distribution of weight and buoyancy.'*
32. What is a compressive strain and a tensile strain ?
33. Show in any graphic way how to combine and arrange ths material
used in the construction of ships so as to give greatest resistance to bending.
34. What kind of ships offer greatest resistance to longitudinal bending,
and which offer least ?
35. Where are the fore and after strains greatest ? Show why.
36. What is the tendency of strains due to rolling motion ?
37. What strains are supposed to be provided for in vessels built to the
requirements of the recognised classifying societies? What strains may a
vessel experience which such rules do not profess to cover?
CHAPTER V.
38. Enumerate the parts of a ship's structure known as transverse framing.
What is the function of transverse framing ?
39. Describe carefully and in detail how the parts which make up a com-
plete transverse frame are connected with one another, and also the various
forms of material which may be used.
40. What is meant by compensation in ship construction ? Give illustra-
tions.
41. Give rules for beam knees.
42. Which are the best beams to fit under iron or steel decks, and also
under wooden decks ? Give illustrations.
43. What depth must a ship be to require two tiers of beams, and also
three tiers of beams ?
44. How may the lowest of these tiers be dispensed with, and state
clearly the compensation made for the loss ?
45. What are web frames ? When and where are they fitted ?
46. State which parts of the transverse framing specially resist the
tendency to *' working," produced by rolling motion.
47. Mention the parts comprising longitudinal framing. What is the
function of longitudinal framing?
48. What means are adopted to secure a good connection between the
longitudinal and the transverse framing?
APPENDIX. 331
49. What is a bar keel ? How are the parts comprising this keel connected t
50. What is a keelson and a stringer ?
51. Sketch roughly the different forms of keels and centre keelsons, and
state which (if any) combination is preferable.
52. What is the garboard strake ? The sheer strake ?
53. How is it that most of the material used in a ship's construction is
reduced in thickness towards the ends?
54. Describe any method adopted to compensate for cutting down a centre
keelson or reducing a stringer plate in width.
55. Describe what provision may be made to resist panting strains, and
also strains from masts due to wind pressure.
56. What are the special characteristics of a three-deck, a spar-decked,
an awning-decked, and a quarter-decked vessel ?
57. Why are bulkheads fitted? Show how they are connected to the
shell plating. To what height are bulkheads carried? How is a recessed
bulkhead made watertight?
58. Show how a bulkhead is made watertight where a keelson or stringer
passes through it.
59. What is a rimer and a drift punch, and their use? Which is the
best form of rivet, and why ?
CHAPTER VI.
60. Define the term *' stability."
61. What are the two factors producing moment of stability ?
62. What is the metacentre ? What is metacentric height ?
63. What is meant by a righting moment of stabilit)' ?
64. State the conditions under which a vessel will float in stable equi-
librium.
65. What is the condition of a ship which is said to be "stiff" or
"tender"?
66. Having given the metacentric height, how can the righting lever be
found, and when is it unsafe to adopt this method ?
67. Give the formula for finding the height of the metacentre above the
centre of buoyancy.
68. What features in the design are most important in influencing the
height of metacentre ?
69. How can stiffness be obtained ?
70. What is a curve of stability, and how is it constructed ?
71. It is usual for the metacentre to fall when the draught is increasing
from light towards the load draught, but on approaching the load it is often
found to rise again. What explanation can be given for this ?
72. Describe clearly the steps of the operation for finding the metacentric
height by experiment.
73. Describe clearly the effect of beam, freeboard, and height of centre of
gravity upon the maximum levers and range of stability.
74. What is tumble home ?
75. State the relation between metacentric height and transverse rolling
motions in still water.
76. Enumerate the resistances to rolling motions.
77. What are bilge keels, and why are they fitted ? What is the danger
among waves of great metacentric height ?
78. What methods may be adopted to obtain steadiness among waves,
and state clearly the condition of a vessel affected by each of these methods ?
79. What is meant by synchronism ? How is it produced and how
averted ? What conditions of loading are most liable to produce it ?
332 APPENDIX.
80. State how it is that similar metacentric heights for load and light or
ballast conditions do not produce similar stability and behaviour at sea.
81. What are the most important considerations in ballasting as regards
the amount, position, and securing the ballast?
82. What is the condition and danger developed by a shifted cargo ?
83. What means may be adopted to prevent a cargo shifting ?
84. State under what conditions a vessel's behaviour and stability may
vary upon a single voyage.
85. State under what circumstances a ship will sink or capsize, owing
to the entry of water into the interior, either through an opening in the
deck or a hole in the side or bottom below the water level.
86. What are the necessary features or conditions of a vessel in order to
be able to carry large sail area ?
87. Enumerate the chief resistances to propulsion,
CHAPTER VII.
88. What is meant by the terms "trim," "moment to alter trim," and
*' moment to alter trim one inch " ?
89. How would you distribute the cargo in the holds of a vessel so as to
produce no alteration of trim in immersing her from the light to the load
draught ?
90. Explain how you would arrange the cargo in a vessel so as to obtain a
definite condition of trim.
91. How is the change of trim estimated, owing to the filling of a fore peak
tank?
92. Explain how to estimate the change of trim caused by an empty com-
partment in the double bottom becoming damaged, and the sea filling the
compartment.
93. Give the formula for ** moment to alter trim one inch."
94. Why is there so great a difference between the height of the longi-
tudinal metacentre and the vertical metacentre above the centre of buoyancy
at any particular draught ?
CHAPTER VIII.
95. What is meant by gross and under-deck tonnage, and what spaces are
included in each ?
96. Enumerate the deductions from the gross tonnage for register tonnage.
97. How is the propelling space deduction in steamers obtained ?
98. When are deep water-ballast tanks allowed as deductions, and when
are they not?
99. How are deck cargoes reckoned as regards tonnage ?
100. What are the important differences between the ordinary tonnage
and Suez Canal tonnage ?
CHAPTER IX.
101. What is meant by the term "freeboard '* ?
102. What are the leading considerations in determining the freeboard for
any particular vessel ?
103. Why have spar-decked vessels more freeboard than three-deckers,
and awning-decked vessels more freeboard than spar-deckers?
104. What effect have sheer, camber, length, and deck erections upon
freeboard ?
APPENDIX A.
105. Describe Rowe's anti-rolling troughs.
I1?]"DEX.
Amidships strength, 60.
Ardency, 214.
Atmospheric pressure, 25.
Awning-deck vessels, 74, 95, 97 ;
Scantlings of, 102, 103.
B
Ballast, Amount and arrangement
of, 166-185; Means to prevent
shifting of, 169 ; Minimum ballast
draught, 180 ; Testing ballast
tanks, 38 ; Water, 169-185.
Beam knees, 54.
Beams, 53, 74, 89 ; Compensation for
dispensing with, 64; Compensa-
tion for loss of, in engine and
boiler space, 76.
Behaviour, Eft'ect of bilge keels upon,
150, 163 ; at sea, how affected, 160;
Alteration of, on a voyage, 161 ;
how affected by arrangement of
weights fore and aft, 163 ; how
affected by arrangement of weights
transversely, 161 ; how affected by
metacentric height, 162.
Bilge, Strengthening of, 53, 56.
,, keels. Effect of, upon rolling
motions, 150.
Boiler stools, 78.
Bosom piece, 51.
Breadth, Extreme, 62.
„ Moulded, 62.
Breast hook, 89, 90.
Bridge over half midship length, 76.
Bridges, Value of, 61.
Bulb angle, 52, 53.
Bulkheads, 97-109 ; Height of, 104,
210 ; liners, 107; longitudinal, 107 ;
Number of, 97 ; recessed, and means
of making watertight, 105 ; stiffen-
ing, 107 ; watertight doors, 108.
Buoyancy, 19, 113 ; afforded by cargo,
203 ; Centre of, 23, 27 ; Curves of
centres of, 28-33 ; effect of camber,
38 ; Effect of entry of water upon,
36 ; Effect of longitudinal bulk-
heads upon, 206 ; Reserve, 22, 26 ;
Wedges of, 33-36 ; forces among
waves, 153-160.
Butts, 51, 58.
Buttstrap, 109.
Calculations {see Contents, pages
271, 301).
Camber, 38.
Cargoes, Homogeneous, 188 ; Shift-
ing, 193.
Cement washing, 76.
Centre of effort, 214.
,, gravity, 14 ; Height of,
128, 132.
Centrifugal force, 154.
Channel bar, 53.
Coefficients, 10, 11.
Collars, 107.
Compensation for dispensing with
hold beams, 54.
Connection of longitudinal and trans-
verse framing, 54-56.
Cosines, Table of, 268-270.
Cotangents, Table of, 268-270.
Countersinking, 110.
Cylinders, Stability of, 121.
Deadweight, 6.
,, scale, 5 ; Relation of,
to type, 91-97.
Deck cargoes. Means to support, 91.
,, erections, Value of, 27.
Decks, Steel, 75.
333
334
INDEX.
Deck weights, Means to support, 91.
Depth, Lloyd's, 62-74 ; moulded, 62 ;
spar- and awning-deck vessels, 62.
Diamond plate, 55.
Displacement, Coefficient of, 10 ;
curve, Construction of, 3-5 ; De-
finition of, 1 ; scale, Vertical, 5.
Double bottom for water ballast, 80,
170.
Draught, after lying aground, 25.
,, Salt and fresh water, 9.
Drift punch, 109.
Engine, Foundation plate under, 79 ;
seat, 76-78 ; space. Strengthening
of, 76 ; trough, 78.
Equilibrium, Condition of, 114 ;
neutral, 115 ; stable, 115 ; un-
stable, 114.
Faying surface, 109.
Flam, 164.
Flare, 164, 200.
Floors, 53 ; Dej.th of, 53, 82, 89 ;
Thickness of, under engines and
boilers, 76.
Foot-ton, 12, 112.
Frame bar, 52.
,, heel, 61.
,, spacing, 51.
Framing, Longitudinal, 40, 57.
,, Transverse, 40, 51.
Freeboard, 7 ; Corrections upon, for
erections on deck, 258 ; for length,
/ 256 ; for round of beam, 258 ; for
sheer, 257 ; Definition of, 251 ;
examples showing how ascertained,
262-267.
Garboabd strake, 61.
Girder, ship. Strengthening flanges
of, 61.
Gravity, 14, 113 ; force among waves,*
154.
Gunwale, Strengthening of, 61.
I
Important terms. Definition of,
62.
Intercostal plates, 78, 81.
K
Keel, 57-60.
Keel scarph, 57.
Keelsons, centre, 58-60 ; Position of,
60 ; Function of, 60 ; N umber of,
75 ; compensation for reduced
depth, 81.
Kinetic energy, 149.
H
Heel piece, 38.
Hold beams, 74.
Lateral resistance. Centre of, 213.
Leeway, 214.
Length between perpendiculars, 62 ;
Extreme, 64-73; Lloyd's, 62;
Standard of, 75, 76.
Leverage, 12.
Loading, 186 ; Eflfect of, upon be-
haviour, 160.
Lug piece, 69, 60.
M
Mast partner, 91.
Masts, Strengthening and fixing of,
to resist strain, 91.
Metacentre, Transverse, 114 ; above
centre of buoyancy. Rule for, 115 ;
Curves of, 126, 127 ; Relation of
design to height of, 118 ; Varia-
tions in height of, 200.
Metacentre, Longitudinal, 232 ; Curve
of, 235.
Metacentric height. Effect of loading
upon, 120 ; how found, 128 ; Rela-
tion of, to wind pressure, 215.
Metacentric heights, similar. Effect
of, at different draughts^ 106 ; sta-
bility, 115.
Metal chocks, 106.
Midship sections, 51, 64-72, 80,
98-102.
Moments, 12 ; Calculation of, 13-15 ;
righting and capsizing, 12.